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t'i'*^      iV; ';' 


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premiere  page  qui  comporta  une  empreinte 
d'impression  ou  d'illustration  et  en  terminant  par 
la  derniire  page  qui  comporte  une  telle 
empreinte. 

Un  dee  symboles  suivents  apparaltra  sur  la 
darniire  image  de  cheque  microfiche,  selon  le 
cas:  le  symbols  — *•  signifie  "A  SUIVRE ',  le 
symbols  V  signifie  "FIN". 

Les  cartes,  planches,  tableaux,  etc.,  peuvent  dtre 
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de  t'angle  supirieur  gauche,  de  gauche  i  droite. 
et  de  haut  en  bas,  en  prenant  le  nombre 
d'images  nicessaire.  Les  diagrammes  suivants 
illustrent  la  mithode. 


1 

2 

3 

1 

2 

3 

4 

5 

6 

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MUCROCOTY   RBOIUTION   TKT  CHART 

(ANSI  and  ISO  TEST  CHART  No.  2) 


1.0 


I.I 


13,0     "«^"  M^^B 


Its 

U 


ia7 

14.0 


1 2.2 
2.0 


1.8 


^  /APPLIED  IIVMGE    Inc 

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\    irjsnsESijfisss:s:^3^ 


A    ]k[AXrAL 


OF 


LABORATORY    PHYSICS. 


wt 


H.   M.   TORY,   M.A.. 

Lnlu>-t>-  m  Mathematics,  McGitl  Umvos-ty.  Moi-.treal: 

Late  Demonstrator  o'  Physics,  McDoti'iul  Physics 

Buiidmg,  McGill  University. 

AND 

F.   H.   riTCHEU,   M.S(  .,    A.M.I.E.E., 

Late  Demonstrator  o*  Physics.  McDonald  Physics 
Building,  McOitl  University,  Montreal. 


FIRST    EDITION. 
FIRST  THOUSAND. 


NEW   YORK: 

JOHN  WILEY   &    SONS. 
London:  CHAPMAN  &  HALL,    LiMiXEa 


T.'^''  '^•i^.s  •'^^■^ss£^s^ir£Si?ss>F:&:^:5^ii::^f: 


Qvt^'^.   '\''V 


Copyright,  1901, 

BT 

H.  M.  TORY. 


KOBHT  eWniMOKtl.  PRIKTKF.   KET  TOIIK. 


:.:a(*^'es^ 


4 
1. 


PREFACE. 

Thk  present  volume  is  iiiteinle<l  as  an  Klenieiitarv  Labo- 
ratory Course  in  SouikI,  M-jht,  Ih-ut,  Mai,nieti>tn,  and  Klec- 
tricity,  and,  with  additional  examples  and  special  exercises, 
constitutes  the  course  in  Elementary  Pliy.>ies  i;iven  at  the 
McDonald  Physics  liuildiiii;,  Mc(iill  University,  .^^)ntreal. 
The  method  of  treatment  is  the  outyrow  th  of  experience  in 
teaching  large  classes  with  a  limited  numher  of  instructors, 
and  the  book  is  offered  to  the  public  with  the  h()])e  tliat  it  nuiy 
be  found  useful  toother  teachers  similarly  situated. 

A  separate  manuscript  was  originally  prej)ared  for  each 
experiment.  The  general  form  of  treatment  was  approved 
of  by  Professor  Cox  and  Professor  Callendar  (when  holding 
the  chair  of  Physics  in  McGill  University),  and  afterwards  by 
Professor  Rutherford.  For  each  experiment  there  is  a  list 
of  references,  a  list  of  apparatus,  a  short  statciueTit  of  the 
theory  involved,  practical  directions,  and  a  tabulated  example. 

The  "References'"  under  each  experiment  are  to  a  num- 
ber of  the  best  American  text-books  on  (ieiieral  Plivsic's,  as 
well  as  to  a  number  of  standard  English  books,  (lenerally 
speaking,  any  one  of  these  will  be  found  to  meet  the  needs  of 
the  student.  The  books  referred  to  are  as  follows :  Elemen- 
tary Text-book  of  Physics,  by  Anthony  and  Brackett :  The 
Elements  of  Physics,  Xicliols  and  Franklin:  Elementary 
Text-book  of  Physics,  Knott :   The  Tlieory  of  Heat,  Preston  ; 

iii 


yp/asBataay^gjsaiawg.gafejWvygi 


IT 


rUEI'ACK. 


Klcmentary  Lessons  in  Klectiicity  and  ^[ugnetisrn,  Silvanus 
Thompson;  A  Text-l)<>ok  of  Physics,  Wutson ;  Physicr.  for 
University  Students,  (.'iirliart;  General  Physies,  Hastings  and 
IJeacli;  Physics,  Advanced  Course,  Parker;  Tlieory  of 
Pliysics,  Ames. 

I'nder  "  Ai>|»aratus  Ileciuireir'  will  he  found  an  exact 
statement  of  the  apparatus  necessary  for  the  particular  ex- 
periment. 

Under  "Theory  of  Experiment"  willhe  found  set  forth  the 
thec)ry  involved  in  the  special  experiment  under  consideration. 
As  most  students  come  to  the  laboratory  with  very  imiH^rfeetly 
formed  ideas  of  physical  theory,  this  portion  of  each  experi- 
ment has  been  found  especially  useful,  as  it  gives  to  the  stu- 
dent a  clear  conception  of  the  j»riiiciples  involved  i)efore  ho 
begins  the  actual  practice  of  the  experiment. 

Under  "Practical  Directions"  will  be  found  just  such 
directions  as  a  Demonstrator  would  give  to  a  student  if  stand- 
ing '  "side  him. 

In  addition,  a  tabulated  example  of  the  observations  and 
results  has  been  added  to  serve  as  a  guide  to  the  student.  In 
cases  where  doubt  might  arise  the  calculations  involved  will 
also  be  found. 

The  examples  have  been  taken  mostly  from  the  work  done 
by  student;^,  and  will  serve  to  give  an  idea  of  the  order  of  ac- 
curacy possible. 

The  "Blank  to  be  tilled  in  by  Student"  has  been  added 
to  enable  the  student  to  keep  a  permanent  record  of  his  work. 
The  results  should  be  first  returned  to  the  Demonstrator  in 
tabulated  form  and  approved  of  before  they  are  entered  in  the 
bo"k. 

Most  of  the  manuscripts  were  prepared  when  Mr.  Pitcher 
and  I  were  fellow  Demonstrators  in  the  laboratories.  On  Mr. 
Pitcher's  retirement  from  the  University  and  my  own  retire- 


uiS^r 


PREFACE.  V 

inent  as  a  teacher  from  tlie  Physical  Dopurtineiit,  the  work 
of  publicaticju  wus  uiulertaken  at  tlie  rcniot  of  the  I'rufossur.s 
in  charjrc.  During  the  pa^t  year  I  iiave  revised  and  n.ni- 
]»leted  tlie  separate  man  user  ipts,  rednein^'  them  t..  the  present 
uniform  pattern.  As  a  result  of  the  method  (.f  treatment 
some  ap])arent  repetitions  occur  under  "  Tne«>ry  of  Kxpiii- 
ment,"  but  I  have  preferred  to  let  these  renuiin,  so  that  ea»  h 
experiment  stands  in  a  sense  complete  hy  itself,  thus  j)ermit- 
ting  the  order  of  work  to  he  varied. 

For  much  lielp  and  nuiiiy  suggestions  in  the  origimil  draft- 
ing of  the  manuscripts  we  are  indebted  to  J'rof.  Callendar,  to 
whom  some  of  the  manuscrii)ts,  especially  those  on  the 
D'Arsonval  galvanometer,  are  due. 

Constant  reference  has  been  had  to  text-books  of  Practical 
Physics,  especially  to  those  of  (ilazebrook  and  Shaw  (which 
work  was  origimilly  nsed  by  us  as  a  text-book),  Stewart  and 
Gee,  Nichols,  and  Kohlrausch  (Physical  :Mea^urements). 

As  most  of  the  proof-sheets  have  been  read  only  by  myself, 
I  doubt  not  that  some  inaccuracies  still  remain,  thoughnone 
I  hope  whieh  can  be  considered  of  any  conscr^uence. 

Especial  thanks  are  due  to  Mr.  II.  T.  Barnes,  D.Sc, 
Lecturer  in  Physics,  for  valuable  assistanee  in  collecting  ma- 
terials for  some  of  the  tabulated  examples. 

II.    ^\.    TOKV. 


McdiLi,  Coi,LEOK,  February  9,  1901. 


Trm^m 


y^'i^ffrre.'^ri'^ss^ 


CONTENTS. 


f  I 


1 
(  I 


1. 

o_ 

3. 
4. 
5. 
G. 
». 
8. 
0. 
10. 


11. 
li. 
1.'). 
11. 

!"!. 

(i. 

1  r. 

18. 
lU 
20 
21. 
23. 

23. 

24. 


SOUND. 

PAOC 

'I'lie  Sonometer 1 

Tlie  l{esonRiice>tut)e — Velooity  of  Sound 4 

Tlie  Si  rcn 8 

'I'lii-  Ci)iiii)avis()ii  of  Forks  liy  Heats H 

Lissnjoiis  Figures  13 

Tht!  W-lociiy  of  Waves  in  a  Stretched  String 17 

The  Fircli  of  H  Fork  l>y  Falling  Plate 19 

Laws  of  Vilirating  Strings,  Melde's  Method 23 

Kundt's  Tube — Velocity  of  Sound  24 

The  Penduluni-chrouograph , gy 

LIGHT. 

Huiism's  Pliotonieter 82 

I' 11  111  ford's  Photometer 34 

Verification  of  the  Law  of  Reflection 3fi 

Mtiisureuicnt  of  tlie  Angle  of  a  Prism,  Pin  Method 40 

|{'f  I  active  Index  of  Gla.ss,  Pin  Method 43 

Kel  racti vc  Index  of  a  Prism,  Pin  .Method   46 

U'adius  of  Curvntiire  of  a  Spherical  Surface  by  S|dieroiiieter 51 

Uiidius  of  Curvature  of  a  Concave  Spherical  Surface  by  Reflection..  54 

Radius  of  (Jurvafiire  of  a  Convex  Spherical  Surface  l)y  Reflection.,  ru 

The  Foctil  Length  of  n  Convex  Lens  by  Parallel  Rays,  Method  I.  . .  60 

The  Focal  I,ength  of  a  Convex  Lens,  Method  II   63 

The  F0c.1I  Length  of  11  Con\-ex  Lens  bv  Changing  Position  of  Lens. 

Method  III   .' 65 

The  Focal   Length  of  a  Convex  Lens  by  the  Size  of  the  Magnified 

Iniaire.  Method  IV.    gg 

The    Focal    Length  of   a  Conctve   Lens    by  Divergence   of   Rays, 

Method  I I  _  70 

vii 


*!''aE5:.!r;Et!:zs'.if3KS^SE^i'3£i^.i 


VIU 


COXTEWTS. 


25.  The  Focal  Length  of  a  Concave  Lens  by  Meana  of  Convex  Lens, 

lf"\     Method  II " 72 

i  26.1(1)  C'onstmctjoi.  of  a  Microscopt.     (2)  Construction  of  a  Telescope.  75 

vJW:   The  Magnifying  Power  of  u  M  iscroscope '. 77 

2b.  The  Magnifying  Power  of  a  Tt-Iescope 81 

29.  The   Spectroscope  —  Mapping   the   Spectrum  — Measuring   Wave- 

lengths   8;j 

30.  The  Angle  of  a  Prism— The  Refractive  I  dex  of  a  Prism  by  Means 

of  the  Spectrometer 89 

31.  The  Refractive  Index  of  a  Liquid  by  Means  of  a  Microscope 92 

HEAT. 

32.  The  Construction  and  Calibration  of  a  Spirit  Thermometer. 94 

33.  Testing  the  Fixed  Points  of  a  Thermometer— Correction  for  Stem 

Ex])osure 96 

34.  The  Coefficient  of  Expansion  o.  a  Liquid  by  a  Weight  Thermometer  100 

35.  Coefficient  ol"  Linear  Expansion  of  a  Solid ]03 

36.  The  Constant- volume  Air- thermometer 106 

37.  The  Constant-pressuie  Air-thermometer Ha 

38.  The  Specific  Heat  of  Copper  and  Zinc,  Method  of  Mixtures 117 

39.  The  Latent  Heat  of  Fusion  of  Ice 121 

40.  Tl  e  Latent  Heat  of  Stt^am 124 

MA(JNET1SM. 

41.  Blue-printing  Lines  of  Force J27 

42.  Mapping  the  Magnetic   Field  around  a  Bar  Magnet,  Moment  by 

Neutral  Point jog 

43.  The  Moment  of  a  Magnet  by  Oscillation  5f(.tliod i;!4 

44.  The  C(imi)arison  of  Moments  by  Oscillation .   136 

45.  The  Moment  of  a  Magnet  by  Deflection  Method 139 

46.  Tiie  Moment  r)f  a  Magnet  by  the  Torsion  Balance  143 

47.  The  Horizontal  Intensity  of  the  ?]artl>'s  Magnetic  Field  i)y  a  Magnet- 

ometer   ^ 146 

48.  Tlie  E(iui valent  Leiiirth  of  a  Magnet ir,0 

49.  The  Compass-box  X'arioiiieter  I'^D 

KLEcruicri'v. 

.lO.  Sine  and  Tangent  Methods  of  Measuring  Currenta 157 

51.  The  Absolute  Measure  of  a  Ciuiint   !();! 

52.  The  F,le<'fro.chemical  Eiiuivalent  of  llydrotren ifi.', 

5:!.  The  Comparison  of  Electro  clifiiiical  !:(|uiviil<-nts 170 

."i4.  'I'lif   Determination  of  tlie   lloii/nntul   C..m|>oMtnt  of  tlie   Eartli's 

.Magnetic  Force  by  Tangent  (iMKi.nouit'ter 17;', 


^^aauiz^^'!)  v'MiiiasagiaM«ciM!wa>i5£  ;^' 


COMA\\TS.  ix 

CXP. 

55.  The  Heductiou  Factor  of  a  Galvanometer. .    ..  ""i^-! 

56.  Ohm's  Law ^'" 

•••••••■••••a ••••••••••.,,,  lT7 

57.  Comparis,,!.  of  Electrical   Kesistances   by  Sine  or  'ranp..I,t'ualva- 

nonifter 

I J  „g 

'  58.  M«i.siirement  of  Hesistances,  B.  A.  Bridge jo, 

59.  Measiireiufiit  of  l{esisiance.s.  Differential  (ial'vanomVt.-r" ." ! iss 

GO,  Siifcilic  Hesistance 

61.  Ki'Mstance  of  a  (iaivanometer  by  Shunting    loi 

62.  \VLeatstone'.s  Bridge  :  (1 )  K.sistance  of  Coil  ]  ',2)  lie.si'  "anrvof  (iaV- 

'  vanr)ineter  ;  (3)  Kesistanro  of  Batteries ^  gg 

63.  ( 1)  To  Verify  Joule's  Law,  JH  =  C^Ji,  (g).    (f,) "to  Find",/ ooa 

64.  (  omi)arison  of  Kesistanc-.,.s.  Ca.ey  Foster  iMetbod "  "  o,)9 

65.  Calibration  of  Slide-wire  Bridge,  Carey  Foster  Method 014 

66.  Variation  o(   Resistance  with  Temperaftre-Determinationof  Tern-  " 

perature  Coefficient 

67.  Measurement  of  Small  Resistances .joi 

^    ^  6b.  .Measurement  of  Large  Resistances ..,[ go- 

I  I!'!'  ^'°"'l'"'«""  "^  Kiectromotive  For.vs.  Tamr'eilt  iialvanomVter 2>'^9 

i  70.  romparuson  of  Electromotive  F.n  es.  Potentiometer  Method       "  " "   030 

71.  CahbrutK..!  of  an  Ammeter  l)y  Gas  Voltameter....  '"   035 

72.  Determination  of  Constant  of  a  Siemens  Electro-dynnm'ometor;  "  ' '  ''is 
7J.  Calibration  of  an  Amn.eter  by  Siemens  Eleclro-dvninnometer        " "   241 

74.  Determination   of   Resistance  of  a   D'Ar.sonval  '(ialvanometer  'by 
Sl'"nting •'  ^^g 

75.  Determination  of  Constant  of  a  D'Arsonval  (Talvonometer  !....!. "   047 

76.  Calibration  of  the  Scale  of  a  D'Arsonval  (ialvanometer .   ..  o^i 

77.  Measurement  of  Potential  Differences  by  D'Arsonval  Galvanometer    255 

78.  Cahbration  of  a  Milli-volt  .Meter '  oi-n 

79.  Determination  of  the  Logarithmic  Decrement  of  a  Galvanometer        265 

80.  The  Absolute  Capacity  of  a  Conden.ser.  Ballistic  Galvanometer. ...     270 
8L  Comparison  of  C.mdensers,  Direct-deflection  xMethod "    '"  275 

82.  Comparison  of  Condensers,  Method  of  Mixtures 078 

83.  Comparison  of  Condensers.  Bridge  Method .'. ogQ 

84.  Measurement  of  El..ctr.miotive  Forces  and  Besistances  of  Batteries'   " 
Condenser  Method '  „„„ 

• *0« 


■r^rrn 


3^  tsr** '  Tgs.'^f .'  •as^a^ijTi 


>m-^sus::^:s3aKt:iii£Htm 


.61^1?'    inf     'ii       ^iiii  Ml  I   II     mill    III  I 


:s^r>t^':*3U«(?;i£;iaK7iAS9sr'-.:^a«^a»TrLS^{! : 


LABORATORY  PHYSICS. 


SOUND. 


I.  TO    DETERMINE    THE    VIBRATION    FREQUENCY  OF 
A  TUNING  FORK  BY  MEANS  OF   A   SONOMETER. 

References — Knott,  p.  261  ;  Hastings  and  IVacli,  p.  563; 
Carliai't,  i)t.  i.  ]>.  186;  Tsicliols  and  Franklin,  vol.  ni.  p. 
160;  Ames,  ]>.  173;  Anthony  and  ]>rac'kett,  p.  165; 
Watson,  p.  ;r.»2:    IJurker,  p.  231. 

Apparatus  Required.  —  A  sonotneter;  a  tuning-fork, 
provided  with  a  resonator;  a  rubber  hammer  for  exciting 
the  fork. 

Theory  of  Experiment — If  a  string  stretched  under  a 
tension  '1\  so  great  that  the  action  of  gravity  may  be  neglected 
in  comparison  with  it,  be  made  to  vibrate  by  drawing  it  aside 
at  one  point  and  then  suddenly  freeing  it,  the  disturbance 
will  be  transmitted  along  the  string  as  a  wave  motion,  the 
velocity  of  the  wave  being  given  by  the  equation 


=  \/l; 


(1) 


where  m  is  the  njass  of  the  string  per  unit  length. 

If  I  be  the  length  of  the  vil»rating  portion  of  the  string, 
and  n  the  vibration  frecpieiu-y  fi.»r  the  fundamental  note,  then 


T' 


2///, 


I    I    II IIIHi   111111111111  'IMl(lll|flHfl     liiJIlill llilHlllil    illi  I  I     il         IBIWIIII      IIMII   l|l|||l||l  lllli  ll 


2 


LABORATORY  PHYSICS. 


and  therefore 


"=W. 


(2) 


In  formula  (2)  all  the  laws  of  the  transverse  vibration  of 
strings  are  included. 

If  the  length  of  the  vibrating  portion  of  t^ie  string  be 
adjusted  till  the  emitted  note  is  the  same  as  that  of  a  tuning- 
fork,  the  vibration  frequency  of  the  fork  can  be  calculated 
from  the  formula. 

Practical  Directions. — We  shall  assume  that  the  usual  form 
of  sonometer,  provided  with  w  'ig;  ts  for  altering  the  tension, 
and  with  a  movable  bridge  for  altering  the  length  of  the 
vibrating  portion  of  the  string,  is  used. 

A  piece  of  piano- wire  of  small  diameter  is  generally  suit- 
able for  the  purpose  of  the  experiment. 

If  the  weight  m  of  the  unit  length  of  the  wire  be  not 
given,  the  wire  must  be  weighed  before  attaching  it  to  the 
sonometer-box,  and  m  calculated. 

Fasten  one  end  of  the  wire  to  the  sonometer-box,  and  the 
other  to  the  attachment  for  holding  the  weights. 

Stretching  the  wire  over  the  pulley,  attach  20  to  30 
pounds  weight. 

Excite  the  fork  by  a  blow  from  the  hannner. 

Vibrate  the  wire  by  snapping  it  with  the  fingers  at  the 
middle  puiiit. 

rontinue  the  process,  ad'  "ting  the  length  of  the  vibrat- 
iiiir  wire  bv  means  of  the  able  bridge,  until  the  strinir 

and  fork  are  in  unison. 

Care  must  be  taken  to  adjust  the  string  so  that  the  funda- 
mental note  is  in  unison  with  the  fork.  To  make  quite  sure 
of  this,  sound  the  first  harmonic  bv  vibrating  the  string  one- 
quarter  of  its  length  from  the  end  and  tcmcliing  it  lightly  at 
the  mi'ldlo  wifli  the  fiiigcM-.     Tiiis  being  the  first  harmonic, 


SOUXI). 


8 


and  an  octave  above  the  fundamental  of  the  strinff,  will 
enal)le  tlie  ear  to  determine  at  once  wliether  tlie  fundamental 
is  being  tuned  to  the  fork  or  not. 

If  it  be  found  that  less  than  one-third  of  a  meter  of  wire  is 
lised  in  the  vibrating  portion  the  tension  should  be  increased 
so  that  the  length  of  the  string  can  be  increased,  otherwise 
the  string  will  vibrate  for  such  a  short  period  that  it  will  be 
almost  impossible  to  make  the  comparison. 

Measure  in  centimeters  the  length  of  the  vibrating  wire. 

lieud  the  stretching  weight  and  reduce  it  to  dynes. 

Calcuhite  ?i  from  formula  (2). 

Repeat  the  observations  three  times,  altering  the  wei<dit8 
each  time. 

Example. — Enter  results  thus: 
m  -  .0424 


Wfiglit. 


28.4 
40.0 
49.0 
5C.r> 


Mfaii  value  of  ;? 


5 

lbs. 

10 

<( 

15 

(  ( 

20 

" 

Tin  nynes. 

2224908 
4449fcil»i 
6674724 
8899632 


128 
127.8 
127.7 
128  4 


127.9 


2'  =  5  X  4r)3.C  X  981  Dynes,        1st  observation. 
1 


n  = 


,/2224908       ,„„   , 
2xl>HlV     .0424-  =  ^28.  1st  " 

Blank  to  he  Jilhd  In  hy  student, 
m  = 


Observation. 

I 

WeiRlU. 

T  in  Dynes. 

n 

Mi'an  value  of  n 

2- 


LA  n  on  A  TOR  T  rilTSICS. 


2.  TO  DETERMINE  TUE  VELOCITY  OF  SOUND  IN  AIR 
BY  MEANS  OF  A  RESONANCE-TUBE. 

References. — Hastings  and  Beach,  p.  562;  Ames,  p.  184; 
Barker,  p.  220 ;  Watson,  j).  367 ;  Aiitliony  and  Brackett, 
p.  161;  Knott,  p.  290;   Carl^art,  pt.  i.  p.  146. 

Apparatus  Required. — A  resonance-tube;  a  tuning-fork;  a 
rubber  hammer;  a  tliermometer. 

Theory  of  Experiment. — If  a  tuning-fork  be  made  to 
vibrate  over  the  open  end  of  a  tubo  closed  at  one  end  and  of 
suitable  length,  tlie  tube  will  act  as  a  resonator,  reinforcing 
the  vibrations  of  tlie  fork.  The  length  of  tube  re(]uired  is 
sucli  that  the  time  it  takes  the  vibration  to  travel  to  tlie 
closed  end  of  the  tube  and  back  must  be  the  same  as  the  time 
of  a  Jialf-vibratiou  ot  the  fork. 

If  -??  be  the  velocity  of  sound  in  air,  I  the  length  of  tl»e 
tube,  n  the  number  of  vibrations  per  second  of  the  fork,  and 
t  the  time  of  a  semi- vibration,  then 

_  J_  _  2^ 

or  V  —  4tnl (1) 

It  is  evident  that  the  fork  will  be  reiTiforeed  not  only 
wlien  the  time  corresponds  to  the  first  half-vibration,  but  will 
also  be  reinforced  if  the  lei-jrth  of  the  tube  be  such  that  the 
time  it  takes  the  vibration  to  travel  to  the  closed  end  and 
back  be  equal  to  tlie  time  of  a  complete  vibration  and  a  half 
or  any  odd  number  of  semi-vibrations  of  the  fork. 

It  is  therefore  evident  that  if  tlie  tube  be  such  that  its 
length  can  be  adjusted,  a  series  of  points  of  maximum  reso- 
nance can  be  found.     Hence 

2x-Pl'  ^^) 


V  = 


f'A.^^VML.  ^LaftAnm^Jiate 


SOUND.  5 

where  a?  is  0,  1,  2,  3,  ct(5.,  c(»rresj)onding  to  tlie  first,  third, 
fifth,  etc.,  semi-vihrution. 

This  formuhv  is  not  strictly  accurate.  A  correction  for 
the  open  end  of  the  tubo  is  necessf,ry.  The  correction  is 
nearly  equivalent  to  adding  to  the  length,  I,  of  the  tube  its 
radiuH. 

TJie  formula  tlierefore  becomes 


V  = 


\n{l-\-r) 
Vj^  1  ' 


(3) 


r  being  the  radius  of  the  tube. 

If  now  the  temperature  of  the  air  in  the  tube  be  t,,  the 
velocity  v,  then  the  velocJty  at  zero,  ^, ,  is  given  by  the 
equation 


or 


4,i(l  4-  r) 


{2x-\-  1)  Vl  -j-  .OirSfSt 


■  w 


Practical  Directions. — A  simple  form  of  instrument  suit- 
able for  the  experiment  consists  of  two  glass  tubes  arranged 
to  slide  up  and  down  in  a  wooden  frame,  the  tubes  being 
connected  at  the  lower  ends  by  a  rubber  tube  (Fig.  1). 

When  the  apparatus  is  partially  filled  with  water,  l)y 
adjusting  the  relative  positions  of  the  tubes  the  water  may  be 
made  to  rise  and  fall  in  either  as  desired. 

Adjust  the  larger  tube  until  the  water  rises  nearly  to  the 
top  of  the  smaller  one. 

Hold  the  vibrating  fork  horizontally  over  the  mouth  of 
the  smaller  tube,  and  adjust  by  means  of  the  larger  the 
height  of  water  in  the  smaller,  until  a  point  of  maximum 
resonance  is  obtained. 


n 


6 


LAUOltATOll  Y  Vll  VS/C  W. 


Ab  this  point  is  not  very  sharply  (k'tinotl,  several  soj»arate 
adjustments  should  bo  niiule,  aiul  tlie  incun  of  the  obst-rv.'- 


-SS7 


''^^[r 


Fig.  1. 


tions  taken.  The  leiij^th,  I,  slioukl  l)e  measured  each  time  to 
1  mm. 

Take  the  temperature,  t,  of  the  air  in  resoiuuice-tube. 

Repeat  tlie  observations  for  third  and  fifth  semi- vibrations 
if  tlie  tube  is  l(»nir  enuujrh. 

A  fork  of  ^TiCi  J).  V.  is  vi-ry  suifMhlc  for  tlu-  expcrimctit. 


*  '^imvL^yy^KkJT^t  if  IT. 


f  ^ 


80UND.  7 

A  suitable  hammer  for  vibrating  can  be  made  b^  iiisL-rting 
a  stiflE  wire  into  a  rubber  bottle-cork. 

Example. — Enter  the  observations  thus: 


/,  Ut  Point. 

t 

f,  -.M  Point. 

t 
15 

/,  3d  Point. 

/ 

31.5 
33.1 
31.7 
31.9 

15 

98.4 
99.0 
99.1 
98.3 

Tub<*  U(ft 
long  enuu^'b. 

Mean  =  31  8 

=  98.7 

= 

_  4_x  256(31.8  +  1.5)  _  .  ,  ,,  •  , 

»«  —  — -:--^==—  =  doSOO,     1st  Point. 


VI  +  .003665  X  15 
_  4  X  256(98.7  -f  1.5) 

3  4  1"+  .00366"x  15 


=  33300,      2d  I'oint. 


Mean  value  of  Co  =  33,'50  ciu.  per  sec. 

Blank  to  he  filled  in  by  student. 


I,  l8t  Point. 

t 

I,  Sd  Point. 

t 

I.  3d  Point. 

t 

Mean  = 

= 

v» 


Mean  value  of  c„  = 


K'j^j-^i  mji.' i/^ts.\  :»^s» 


-frii  T7  J   ■-  *  :jf  <ik^f  1 


«!^«;^fifiib6=  ajvnMS'aadfcTC£.4?<;aiBie^^ 


8 


LAUOHATouY  rinsias. 


i 


3.  TO  DETERMINE  THE  FREQUENCY  OF  THE  NOTE 
EMITTED  BY  AN  ORGAN-PIPE,  BY  MEANS  OF  THE 
SIREN. 

References. — Watson,  p.  ;57r»;  Antlidiiy  uiitl  P.iiu'kcft, 
p.  It!.");  Hiistiiii(s  uiid  IJi'ach,  i».  ."il'i ;  Aiiifs,  p.  ir»(»;  Kimff, 
\K  2711;  Nichols  and  Kraiikliii,  vol.  ni.  p.  I."»();  Hiirktr, 
p.  t>lT. 

Apparatus  Required. — A  .-iivii  with  .siiitiil)l(3  Hpeed-^ov- 
iTiior;  ail  ori;:iii-[)ipi'  ami  timiiii;-fork  of  approximutcly  the 
same  fiH-tpu-ncv ;  a  largo  vasomotor  and  a  pair  of  Ih-IIows  for 
tilliiijrit;  an  experinieiital  oriran-ltellows  for  fnriii.ihiiig  the 
Mast  for  tiie  orpiii-pipe ;  a  |>rc'ssiire  ::;aiii;e;  nihlit-r  connecting 
tubinij;;  a  sii})plv  t>f  weights  for  loading  bellows;  a  stoj)- 
watch. 

Theory  of  Experiment. --If  the  air  in  an  organ-pipe  be 
excited  bv  a  blast  of  con.-tant  prosure,  and  a  >iren,  having  a 
6j)eed  t>f  /I  revolutions  pur  second  while  receiving  its  impulse 
through  y>  hole-s  per  revolution,  lie  brought  either  into  uni.suii 
with  the  note  of  the  [>ipe  or  to  ditl'er  from  it  by  a  known 
number  of  beats,  ',  per  second,  the  fre«piency  Foi  the  organ- 
j)ipe  can  be  deteniiinetl. 

For,  if  iti  unison  with  the  siren,  /•'=y*«, 
or  if  licatiiig,  /'=  j,u  _[-  /,, 

If  S(_>nie  means  be  employed  by  which  tlio  revolutions  of  the 
siren  can  be  kept  cou-tant  so  that  tin-  beats  can  be  counted, 
for  a  sutficient  time,  the  above  tlieory  can  be  realized  in 
practice. 

Practical  Directions. — Select  an  organ-pipe  and  connect  it 

to  the  bellows. 

Adjust  the  pressure  of  the  blast  by  weights  till  the 
fiindament,a!  note  is  obtairied. 


-:s:uLf«isL  .Tir  ^  ^ 


i 


SOUND. 


9 


Contucf   tlio  fffot-lKjllows  fo  flie  paKometer  ami   force  it 
full  .if  nil-. 

(.'oniKct  till!  {(iisornctor  to  tlio  sirt-ii  and   pressiirc-^iiij^o. 
JSct;  that  thu  hi»oe(l-couiiter  of  the  Kircii  I'li^a^'t's  in   tlio 
worm  carried  l*y  the  s|iiiidle. 

Set  the  or^'aii-j»i|)e  and  siren  Koundinij,  and  wei^dit  the 
g:iHornetcr  till  the  siren  gives  apitroxiniately  the  note  <.f  the 
organ-pipe  without  consuming  ni(»re  air  than  can  easily  he 
Hupplied  I.J  the  l.cllows  working  contstantly. 

liy  adjusting  the  speed-governor,  hring  tlie  frequency  of 
the  Hiren  up  or  down  as  re<juired,  till  the  heats  are  fairlv 
coiiBtant  for  2(ioo  or  ko  revolutions  and  slow  enougli  to  he 
easily  counted. 

Count  the  total  nuinher  of  heat.^  during  l(l(i(»  or  iiOO(( 
revolutions,  timing  the  revolutions  liy  the  stop-watch. 

Calculate  tlie  frecjueney  of  the  organ-pipe  from  the  ►■  d 
formula  given  above,  ad<ling  or  suhtnicting  the  heats  ac>  d- 
ing  as  the  siren  was  brought  up  or  down  to  l)eat  with  the 
organ-pipe. 

Take  several  observations,  and  average  the  calculated 
results. 

Check  the  residt  ]>y  comparing  the  ]>i])e  Vv  ith  a  standard 
tuning-fork  of  nearly  the  same  period. 

This  may  ])e  done  by  the  method  of  beats,  thf  fork  being 
loaded  to  find  which  note  is  higher. 

Precautions. — Do  not  work  the  bellows  with  jerks  or  thev 
may  burst. 

Be  careful  tliat  the  gasometer  is  never  hard  up  against 
the  stop  at  the  toj)  of  its  gauge  or  the  water  will  be  forced 
out  of  the  gasometer  and  gauge. 

See  that  the  siren  is  well  oiletl,  and  the  i>ivot  bearings 
proj)erly  adjusted. 

Note. — h\    this   cxpcriineni:     the    greatest    diiJicuilv    wa«j 


TiLiVT'^idflR  ^:tn 


10 


LA  JiOKA  TOR  Y  Pll  YSIVS. 


II 

f 


encouiiturud  in  ki'tping  the  s|K't'«l  of  tin-  hirni  Kuftlcirntly 
con»tunt  tlurii)^  olnjcrvation.  For  this  ii  h|»ft'«l-i]j()vt'riior, 
siiijilar  to  those  urtc'<l  iti  electric  power-supply  iiu-terK, — 
notably  thoso  of  Terry  <k  Klihu  Thoiniwou,— wiw  eiii- 
ph)ye(l. 

It  limy  8eeii»  that  the  list  of  appuratus  given  above  Ih 
nither  an  elaborate  one  for  the  iK-rformuiiee  of  thii*  e.\|)eri- 
ineiit,  but  it  was  found  iinpofaible  to  obtain  good  results  with 
the  apparatus  usually  employed. 

Example. — F.nter  results  thus: 


81r«u  Kevoliitioiia. 

Thiif. 

Ii<>«(i(. 

1.-5 

KrtHiiieiioy. 

1500 
lOUO 
1000 

4:t.4" 
80.0" 
2y.3 ' 

-  217 
-f  486 

-  -iio 

St:) 

ftlO 
607 

Meat! 

value  of  i'' 

MO 

Blank  to  he  jf I  led  in  hy  student. 


Siren  RavolutionH. 


Time. 


Bvatn. 


Mi'au  viiltie  <jf  F. 


FrMjueiiejr. 


ti(H  yi>. 


11 


4.  TO  COMPARE  THE  FREQUENCY  OF  TWO  NEARLY 
IDENTICAL  FORKS  BY  BEATS. 


i 


References.— Marker,  p.  US'J ;  Wiitson,  [).  I:.'*;;  Aiitlumy 
uiid  Uriickett,  p.  \M\  Curliart,  j)t.  1.  |>.  l.'.'.t  (4);  Kiiott, 
|».  2^«>;  Ni(tliols  uiid  Kniiikliii,  pp.  l.'jo,  I7."»;  Aim-s,  pp. 
14»;{,  l.si>;    IIiLstinj^K  a!nl  l»t'u<-li,  p.  kni'l. 

Apparatus  Required.  -Two  forks  of  nearly  the  same 
j)iteli,  iiiouiite<l  on  siutablo  resonators,  or  two  identical  forks 
anil  11  pair  of  weights  for  loading  one  of  them.  The  weights 
should  be  provided  with  reference-points  for  the  determina- 
tion of  their  positions  on  th"  prongs  of  the  forks.  In  adtlition 
a  ruhher  hammer,  a  stop-M     eh,  a  centimeter  scale. 

Theory  of  Experiment. —If  tvvo  notes  of  nearly  identical 
pitch  be  soun<led  together,  a  peculiar  tluctnating  etfect  is 
produced.  Alternate  intervals  of  com])arative  silence  and 
bursts  of  sound  are  heard.  These  bursts  of  souiul  are  called 
beats,  and  the  notes  are  said  to  beat  together. 

Let  the  fiC4Uency  of  the  forks  be  )\  and  /*,  per  second. 


Then  n,  =  //,  +^), 

where  jr>  is  the  number  of  beats, 


or 


X 


(1) 


(2) 


where  X  is  the  number  of  beats  heard  in  t  seconds. 
Kor  while  the  lirst  fork  makes  //,  vibrations  the  other  makes 
p  more,  and  therefore  in  l/p  of  a  second  the  second  fork 
executes  one  whole  vibration   more  th.in    the  other.      At  the 


12 


LABOIUTORT  PHYSICS. 


< 


end  of  tlmt  time,  therefore,  the  Bound  will  be  reinforced,  as 
well  as  at  the  end  of  every  succeeding  \/p  part  of  a  second. 
Midway  between  these  points  the  second  fork  has  just  gained 
a  half  vibration  on  the  other,  the  two  forks  are  in  opposition, 
and  there  will  therefore  be  an  interval  of  silence. 

It  follows  that  if  the  number  of  beats  or  loud  points  be 
counted  in  a  given  time,  the  difference  between  the  frequen- 
cies is  completely  determined. 

Practical  Directions. — It  is  more  convenient  to  have  one 
of  the  forks  driven  electromagnetically.  If  such  a  fork  is 
available,  it  can  very  well  be  used  as  tho  standard.  Load  the 
other  fork  near  the  ends  of  the  prongs  by  means  of  the 
small  weights  provided,  until  the  beats  are  such  as  can  be 
easily  counted. 

Count  the  time  of,  say,  20  beats,  if  the  loaded  fork  vibrates 
long  enough.  IVfeasure  the  distance  of  the  weights  from  the 
ends  of  the  prongs  and  calci'.late  the  difference  between  the 
forks  by  foniiula  (2). 

There  will  be  overtones  immediately  after  the  excitement 
of  the  loaded  fork;  these,  however,  soon  die  away,  and  at 
any  jite  do  not  much  interfere  with  the  perception  of  the 
beats. 

To  detei-niine  whether  the  loaded  fork  is  flatter  or  sharper 
than  the  standard,  raise  the  loads  a  very  little. 

Redetermine  the  beats  per  second,  and  if  there  are  fewer 
to  the  second,  the  loaded  fork  was  higher;  if  mwe, vice  versa. 

If  ilie  forks  are  not  identical,  load  the  higher  one  until 
no  beats  are  heard. 

Measure  the  distance  of  the  loads  from  the  ends  of  the 
prongs. 

The  gradual  dying  away  of  the  note  nmst  not  be  con- 
founded  with  the  very  slow  beats  which  occur  as  the  forks 
a])])roach  unison. 


i  ! 


SOUND. 
Example.  — Enter  results  thus : 


13 


Frequency  of 
Standard. 

Distance  of  Weight 
from  End. 

6  cm. 
5.5" 

4.5" 

Time. 

Beats. 

Frequency  of 
Lo.uled  Fork. 

512 

20" 
25" 

50 
45 
10 

514.5 
514.0 
or,\4 

Blank  to  he  filled  hi  hy  ntudent. 


Frequency  of 
Standard. 

Distance  of  Weight 
from  End. 

Time. 

Beats. 

Frequency  of 
lA>atlid  K</]k. 

5.  OPTICAL  TUNING — TO  COMPARE  THE  FREQUENCIES 
OF  TWO  NEARLY  IDENTICAL  TUNING-FORKS  BY 
LISSAJOUS  FIGURES. 

References. — Watson,  p.  400;  Harlior,  p.  2r>2;  Ilastiiiirs 
aiul  Beach,  pp.  529  and  571 ;  Nichols  aiul  P^ranklin,  vol.  in. 
p.  152;   Ant]>'>;iy  uiul  Brackett,  p.  ISO. 

Apparatus  Required. — A  pair  of  identical  tuniiifr.fork.s 
(wiMi  a  frequency  of  ahout  100  I).  V.)  ]>rovidod  with  mirrors 
and  supports;  a  dark  lamp  with  a  pin-hole  in  the  chimney;  a 
telescope;   a  ruldter  exciting-hammer;   a  stop-watch. 

Theory  of  Experiment — The  theory  is  suhstantially  iden- 
tical with  that  of  tlie  ])recedini;  experiment  (Comparison  of 
Forks  hy  Beats),  the  only  difference  being  in  the  method  of 
observation.  The  beats  in  this  case  are  detected  with  the  eve 
instead  of  the  ear. 


\ 


u 


/  I iiouA ion y  I'liysivs. 


W 


Practical  Directions.— ( 1 )  Composition  along  the  Same 
Straiy/it  Line. — Clamp  the  forks  to  their  supports  so  that 
tlioy  may  vibrate  in  the  same  plane. 

Bring  up  the  lamp  to  about  a  meter  from  one  of  the 
niin-ors,  and  adjust  its  i)osition  so  that  an  iraage  of  the 
illuminated  pin-hole  is  seen  l)v  the  eye  when  plaeed  level 
with  the  pin-hole  and  about  one-third  of  a  meter  at  one  side 
of  it. 

I'lace  tiie  other  mirror  to  face  the  former  at  about  one 
w.vtvv  distance,  and  so  that  the  image  of  the  pin-hole  as  seen 
in  the  former  is  intercepted  bj  the  latter. 

riace  the  teleseop  •  at  about  four  meljrs  from  the  second 
niii-ror,  and  focus  it  on  tiie  image  seen  in  this  mirror.  The 
image  as  secTi  in  the  telescoi)e  may  be  a  triHe  blurred  owing 
to  defects  in  the  mirrors. 

If  possible,  clamp  the  supports  of  the  forks  livmlv  to  the 
table,  or  if  not,  the  supports  nuist  be  held  tightly  by  tlie  hand 
when  ex''iting  the  forks,  to  ])revent  them  mo\in<'. 

Excite  each  of  the  forks  by  a  blow  from  the  liammer. 
Il  the  forks  are  in  unison,  a  luminous  straight  line  of  very 
gradually  dimim'shing  length  will  be  seen  in  the  telescope. 
This  image  reduces  eventually,  on  the  cessation  of  both  forks, 
to  the  image  of  the  pin-hole,  without  having  undergone  any 
elongation  whatever  from  the  beginning. 

Xow  load  one  of  the  forks  and  re-excite  them  both. 
A  ftraight  line  of  periodically  varying  length  will  be 
seen.  If  the  vibrations  of  the  forks  have  equal  ami)litudes, 
the  length  will  vary  from  a  iruTc  point,  the  original  image  of 
the  pin-hole,  to  a  line  whose  length  is  equal  to  the  masjniiied 
sum  of  the  amplitudes. 

The  poi?it  corresponds  to  the  interval  of  silence  in  audible 
beats,  ai:il  the  long  line  to  tlie  burst  of  sound. 

:f  the  amplitudes  i.re  imt   the  .sune,  a  line,  equal  to  the 


■^ 


SOiM). 


15 


magnified  difference  between  the  amplitudes,  will  he  observed 
to  be  the  niinimum  length  of  the  fluctuating  line.  This 
accounts  for  the  period  of  only  comparative  silence  observed 
in  audible  beats. 

Count  fifty  of  these  variations  from  point    to  point   or 

iiinimum  length  to  minimum  length,  and  calculate  by  the 

>rniula 


ii,  -  », 


the  difl'erence  between  the  forlcs,  where  «,  and  v^  are  the 
frequen  'js  of  the  forks,  and  A^  k  the  number  of  beats  in 
the  time  t. 

The  time  between  any  two  consecutive  minimum  lengths 
corresponds  to  the  time  of  one  andil)le  beat. 

Measure  the  distance  of  the  load  index  from  th.  ond 
of  the  fork-prong.  Repeat  the  observation  several  ...aes, 
changing  the  position  of  the  load  in  each  case. 

(2)  Composition  at  Rhjld  vl«^A'.v.—  Without  altering  the 
load,  turn  the  forks  in  their  supj)urts  so  that  they  may 
vibrate  at  right  angles.  This  is  mo^t  easily  done  by  turnino- 
thorn  to  vibrate  at  4.>°  to  the  table,  the  axes  of  the  mirrors 
being  in  the  same  horizontal  ])lane. 

Adjust,  as  before,  until  the  image  from  the  .  ond  mirror 
is  seen  in  the  telescope.  If  the  forks  have  only  slightiv 
different  periods,  a  figure  will  be  seen,  changing  from  a 
straight  line  at  4.")'  to  the  horizontal,  through  an  ellipse,  to  a 
straight  line  at  right  angles  to  the  former  line,  and  then 
through  another  ellipse  back  to  the  original  line,  see  Fig.  2. 

HDOOHHOOS 

Fig.  3. 


16 


LABORATORY  PHTStCS. 


The  time  taken  to  make  a  complete  cycle  is  the  time  of 
one  beat. 

As  in  (1),  count  fifty  of  these  complete  cycles.  They 
thould  be  found  to  correspond  with  the  periodic  changes  in 
the  previous  comparison. 

liepeat  the  observations  with  loads  in  same  positions  as 
in  (1). 

(3)  Procure  two  forks  which  are  not  identical,  and  load 
the  higher  one  to  unison  w-ith  the  other  by  observing  when 
there  is  no  periodic  change  in  the  figure. 

Kecord  the  |)osition  of  the  load. 

Precautions. — Do  not  touch  the  mirrors. 

On  no  account  is  the  fork  to  be  excited  by  striking  the 
prong  carrying  the  mirror. 

Example  — Knter  results  thus: 


Oist 

iiice  of  r^oati 

from 

Kiiil  of  Koik. 

(1) 

3.5  cm. 

(2) 

4  cm. 

m 

5  cm. 

(4) 

(i  cm. 

(•'■») 

7  cm. 

Perioiiic  Cliiiii;;e.s. 


Time. 


50 
50 
50 
50 
50 


80.0' 

00.  a" 

40.4" 
20.0" 
10.4" 


Distance  of  IjoaA 
from  End  of  Fork. 


Blank  to  he jiUed  hi  hij  i^iuihnt. 

Periodic  Clianges  Time. 


?i,  -  )i, 


.6 

.H 
1.35 
2.5 
4.8 


SOUND. 


17 


6.  TO   DETERMINE   THE  VELOCITY   OF   WAVES   IN   A 
STRETCHED  STRING. 

References — Watson,  p.  358 ;  Knott,  p.  261 ;  Hastings 
and  Ik'acli,  p.  523;  Nicliols  and  Franklin,  vol.  in.  p.  161; 
Ames,  p.  171. 

Apparatus  Required — A  long  steel  wire;  a  stop-watch; 
a  pulley;  wei<rlits  for  varying  the  tension;  a  tape-nieasnre. 

Theory  of  Experiment — When  a  stretched  .string  is  made 
to  vihrute,  tlie  velocity  of  the  wave  motion  along  the  string 
is  given  by  the  ecpiation 


y  7>i 


(1) 


where  T  ia  the  tCTision,  and  ?»  the  mass  per  unit  length. 

If,  therefore,  the  tension  and  unit  mass  be  known,  the 
velocity  can  be  calculated. 

If  the  time  of  transmission  of  the  wave  from  one  end  of 
the  string  to  the  other  l»e  ol^served,  the  velocity  calculated 
from  (1)  can  be  veritied. 

Thus  if  ;  be  the  length  of  the  string,  t  the  time  of  trans- 
miasion  of  a  wave  from  one  end  of  the  string  and  back,  then 


11 


V  = 


(2) 


Practical  Directions — Weigh  a  known  length  of  the  wire, 
and  find  )/i. 

Fasten  one  end  of  the  lotig  wire  to  the  wall  of  the  room, 
passing  the  other  end  over  a  pnllcy  fixed  some  distance  away. 

To  the  end  which  passes  over  the  i)ulley  fasten  an  attach- 
ment for  holding  weights,  and  put  uii  a  weight,  W,  of  abont 
one  kilogram. 


I 


\u 


18 


LABORATORY  PHYSICS. 


Strike  the  wire  lightly  near  the  end.  A  wave  motion  will 
be  now  transmitted  along  the  wire  and  back. 

Place  the  finger  on  the  wire  about  one  inch  from  the 
pulley.  The  return  of  the  wave  can  be  distinctly  felt  by  the 
finger.    The  return  of  the  wave  can  also  be  observed  by  the  eye 

Start  the  stop-watch  just  as  the  first  pulsation  is  felt,  and 
take  the  time  of  fifty  returns. 

Measure  the  length  of  the  wire  in  centimeters. 

If  the  length  be  measured  in  feet,  reduce  to  inches  and 
multiply  by  2.U  for  centimeters. 

Expresg  the  tension,  7",  in  dynes. 

If  the  veight  be  in  pounds,  multiply  by  456.3  x  981 
for  dynes. 

Calculate  v  from  the  formula 


V  =  a/~. 

y   m 


Calculate  v  from  the  observation  of  fifty  returns. 
Repeat  the  observation  three  times  with  diflerent  weights. 
Example — Enter  the  results  thus: 


Obs. 

m 

I 

Time  of 

Fifty 

Returns. 

T 

vfrom 

Oboerva. 

tions. 

vfrom 
m' 

9462 

7089 

1st  cba. 
1   2(1  obs. 

I 

.02275 

.0'.'275 

1938 
1938 

20.5" 
27.2" 

2032622 
1136471 

9452 
7171 

Blank  to  be  filed  in  hy  student 


Obs. 

1 

»i 

I 

Time  of 

Fifty 

Returns. 

T 

vfrom 
Observa- 
tions. 

1 
tifrom 

III' 

~~ 



souyD. 


19 


I 


•3 


7.  TO  DETERMINE  THE  PITCH  OF  A  FORK  BY  THE 
TRACE  OF  ITS  VIBRATION  ON  A  SMOKED  FALLING 
PLATE. 

References. — Darnes'B  l*ractical  Acoustics,  p.  75. 

Apparatus  Required. — A  tuning-fork  of  fairly  high  fre- 
quency rigidly  fixed  to  a  buitaMu  !3Ui)i)()rt ;  a  suitable  '••lass 
l)late;  a  pair  of  dividers;  a  centimeter 
scale;  a  hog's  l)ristlu;  a  plucker  for  vibrat- 
ing the  fork. 

Theory  of  Experiment — If  a  tinukcd 
glass  i)late  be  let  fall  freely,  so  as  to  re- 
ceive the  trace  of  a  vibrating  tuning-fork, 
the  trace  on  the  j)late  will  be  a  sinuous 
line.  The  vibrations  will  be  very  close  at 
the  bottom  of  the  plate,  lengthening  out 
toward  the  top,  jirovided  the  plate  at  start- 
ing is  in  contact  with  the  tracer  on  the 
fork,  due  to  the  slow  motion  of  the  plate 
at  first. 

Suppose  at  starting  the  tracer  of  the 
fork  be  at  A,  and  that  the  vibrations  can 
be  counted  between  the  p.jints  B  and  C. 
Denote   the   length   AB  by   ^S",  and   AC 

If  t  be  the  time  it  would  take  the  point  B  to  fall  to  th« 
tracer,  then 

'S'  =  h/t' (1) 

Similarly, 

^S  =  h^r\ (2) 

^.  being  the  ti«ie  it  takes  the  point  ('  to  reach  the   tracer. 


Fig.  y. 


^1 


hi 


20 


Hence 


LAJiOUATORY  PHTSIC8. 


,       <_     /'-iS,         /Is 

where  t,  ^  t  k  tlie  time  it  takes  the  tracer  to  pass  from  B  to 
C 

If  V  be  the  number  of  vibrations  between  B  and  ^,  then 

tlje  vibration  frequency  of  the  fork 
is  given  bj  the  equation 


and 


and  therefore 


n  = 


V 


t,  -  f 


•     (5) 


Since  v  can  be  counted,  S  and  S, 
measured,  g  is  known,  n  can  be 
calculated. 

Practical  Directions Clamp  the 

fork -stand  to  the  table.  Fasten  a 
oristle  to  tlie  fork  at  an  angle  down- 
ward of  about  45°. 

Smoke  the  glass  plate  by  passin*,' 
it  rapidly  back  and  forth  through  a 
smoky  paraffine-lamp  flame.  The 
glais  plate  sliould  be  quite  thick,  so 
as  to  make  it  strong  and  compara. 
tively  heavv. 

Hang  the  plate,  by  means  of  a  loop  of  cotton  thread,  to 
the  supports  provided  for  the  purpose. 

Adjust  it  carefully  so  that  it  just  touches  the  bristle  when 
hanging  vertically  with  its  .u.ok  .d  surface  in  the  plane  of 


Fio.  4. 


80  um). 


tl 


m 


vibration  of  the  fork.     Fig.  4  shows  apparatus  when  com- 
plete. 

Set  the  fork  vibrating  by  gently  pulling  off  the  plucker. 
If  the  plate  dance  about,  its  plane  is  not  parallel  to  the  plane 
of  vibration,  and  must  be  adjusted. 

When  properly  adjusted,  sever  thecvspension  by  touching 
it  midway  between  the  supports  with  a  lighted  taper. 

A  clear  continuous  trace  will  now  be  on  the  plate  if  the 
adjustments  have  been  made  with  sufficient  care. 

Select  two  points  corresponding  to  B  and  C,  between 
which  the  vibrations  can  be  counted. 

Measure  the  distances  S  and  5,  between  the  first  point  of 
contact  and  the  points  B  and  C. 

Count  the  vibrations  between  B  and  C. 

Calculate  n  from  the  observations. 

Repeat  the  observations  three  times. 

Example. — Enter  results  thus : 
g  =  981. 


Observations. 

S 

Si 

V 

n 

1st 
2d 
Sd 

1 
1 
1 

10 
95 
10.3 

106 
103 
108 

1075 
1080 
1074 

Mean  vi 

line  of  n 

1076 

Blank  to  he  filled  in  hy  student. 


Observation. 

S 

s. 

V 

n 

l8t 

2d 

3d 

Meaa  vt 

ilusof  >i 

93 


LABORATORY  PIIT8ICS. 


8.  LAWS  OF  VIBRATING  STRINGS. -MELDE'S  METHOD. 

pp.  173-1 7;>;  Nichols  and  Franklin,  p.  IGo-  Haatin... 
and  Reach,  p.  5rt3;  Carhart,  pt.  i.  p    ls8  ^ 

with  cord  attaclunent;  a  snmll  pulley  fixed  to  an  upright  stand 
80  that  a  cord  can  he  stretched  over  it ;  son.e  snJl  weights ;  a 
piece  of  hnen  thread  or  small  silk  cord 

to  ^^17  of  E-Periment._If  a  string  of  length  I  be  nmde 
to  vibrate  under  a  tension  T,  we  have  seen  that  the  laws  of 
vibration  are  expressed  by  the  e.pmtion 


n 


(1) 

Where  n  is  the  number  of  nbrations  per  second,  /  the  half 
wave,e„gth  of  the  vibration  in  the  string,  7'  the  t^.sion,  and 
m  the  mass  per  nint  length. 

.tJL^n  -«««l'ed"to  the    prong    of  a    tuning-fork   be 

vibrating,  the  cord  between  the  pulley  and  the  fork  will  be 
thrown  into  vibrating  segments,  as  shown  in  Fig.  5,  when 
Its  length  is  properly  a<ljusted. 


Pi  (I.  5. 
(1)  The  length  of  the  string  between  the  two  successive 
nodes  gives  the  value  I;   therefore  ;^  the  vibrating  fre.n.ency 
of  the  fork,  can  be  calculated,  since  T  and  m  are  known 
quantities. 


li 

II 


SOUND. 


•23 


(2)  Since        n 


and  also 


then 


or 


V 


^^=27. 


in 


T 


111 


r 

r 


for  a  tension  ST, 
'    for  a  tension  T, , 

->/ .' 


(2) 


1      IT 
By  varying  the  weiglii-s  therefore,  the  law  n  =  ^^\/  — 

can  be  experimentally  verified. 

Practical  Directions. — Weigh  a  known  length  of  the  string 
and  thus  find  m,  the  mass  per  centimeter. 

Attach  the  cord  to  the  prong  of  the  fork,  and  stretch  it 

over  the  pulley. 

Attach  30  or  40  grams  weight  to  the  end  of  the  cord. 

fe. .  the  fork  vibrating. 

Measure  the  length  of  the  string  between  several  nodes, 
and  obtain  the  average  length,  I. 

Observe  the  weight  on  the  string,  and  reduce  to  dynes. 

Calculate  n  from  the  formula 


11 


_l     /T 


Now  vary  the  weights  three   different  times,  and  repeat 
the  observations  for  I. 


Then 


Example.— Enter  results  thus : 


Obi. 
1st 

r 

I 

n 
512 

T 
W 

760 
767 
768 

2d 

'•••WW       1         j'.:.vu 

8d  

88290 

10.75 
I'Jilled  in 

Blank  to  h 

hy  student. 

Ob«, 

T 

I 

n 

T 

. 

i! 


9  TO    DETERMIHE    THE    VELOCITY   OF    soiiMn    r» 
VARIOUS  MEDIA  BY  MEANS  OF  koNDT'S  TUBE.' 

and  !•  a„ki,„  vol.  ,„  ,,.  i,,o;  Crlrnrt,  ,,t.  ,.  ,,.  210;  Ames, 
p.    85;  iraatmgs  and  Head,,  p.  5til ;  Anthony  and  Braekett 

Apparatus  Required. -Kundt's  tube  with  8o,»e  fine  light 
powder,  such  ae  cork-filings;  a  wet  silk  cloth;  a  centinieL 
scale,  a  thermometer;  a  drying-tube ;  a  meter  or  so  of  gas- 
tubmg;  a  pair  of  bellows.  ^ 

K„Ji^''T  1*^  ^^P«"°^«'^t-If  the  apparatus,  arranged  as  a 
Knndt  s  tube,  be  supported  horizontally  and  some  light 
powder  evenly  distributed  over  the  bottom  of  the  tube  the 
powder  wdl  arrange  itself  into  heaps  when  the  rod  is  ruLbed 
Buthciently  to  emit  a  note. 


80  VXD. 


25 


Tho  rubbing  produces  loiigitiuliiml  vibratJorw  in  thu  r<)«l, 
which  are  cuminuiiicated  to  the  air  in  the  tijl>e  m  coiiipn-^- 
Bious  and  rurefuctiona.  The  iM>wder  i.s  forced  away  from  the 
places  of  motion,  tiio  loopH,  to  the  poiiitn  of  re^t,  the  nodes. 

If  the  rod  be  rigidly  fixed  at  its  centre  by  a  clamp,  its 
ondrt  will  be  at  tho  middle  of  consecutive  loops,  the  clamp 
bein;;  at  tho  intcrveiung  node. 

The  length  of  tho  rod  is  therefore  ecpial  to  one-half  of 
the  wave-length  of  tho  note  emitted.  Denote  the  length  of 
the  rod  by  /.  The  distance  from  heap  to  heap,  r/,  is  e^ual  to 
one-half  of  the  wave-length  of  the  same  note  in  the  gas. 

These  lengths  are  described  in  e«pial  times,  since  the  gas 
in  the  tnbe  vibrates  in  muson  with  the  rod. 

The  velocity  of  sound  in  any  medium  is  equal  to  the 
wave-length  multiplied  by  the  number  of  vibrations  per  sec- 
ond.    Therefore 

I 

5' (1) 


V, 

V. 


V,  and  V,  being  the  velocities  in  the  rod  and  gas,  respectively. 
Knowing  the  temperature,  ^„  of  the  air  in  tiie  tube,  the 
velocity  in  it  may  be  obtained  from  the  formula 

r,  =  33250  ^1  -f  .Ou3»i057, ....     (2) 

33250  being  the  velocity  at  0"  C,  and  therefore  v,  can  be 
calculated. 

Practical  Directions.— See  that  the  tube  is  clean  and  dry. 

Clamp  the  rod  in  the  middle. 

Pull  out  the  adjustable  plunger,  and  shake  into  the  tube 
either  dry  cork-filings  or  amorphous  silica. 

Replace  the  plunger,  and  support  the  whole  horizontally. 

The  powder  should  lie  in  a  thin  coating  along  the  bottom 
of  the  free  part  of  tho  tu!)e. 


26 


LABOR ATOIiT  PHYSICS. 


Open  both  stop-cocks  and  connect  one  of  them  to  the 
bellows  through  a  drying-tube. 

Force  dry  air  in  for  some  time  before  closing  the  cocks. 

The  rod,  if  glass,  may  be  excited  by  stroking  its  free  half 
with  wet  silk ;  but  in  the  case  of  brass  or  other  metals  resined 
chamois  will  be  found  better. 

If  after  the  first  rubbing  the  nodes  in  the  tube  are  not 
well  defined,  adjust  the  length  of  the  column  of  air  by  the 
plunger  and  repeat  the  rubbing.  Continue  the  adjustment 
u:  til  the  nodes  arc  sharply  defined. 

When  the  nodes  ha>e  become  sharj),  measure  tlie  distance 
to  each  from  one  end  of  the  tube.  Subtract  the  distance  of 
the  middle  one  from  the  first,  the  distance  of  the  next  one 
beyond  the  middle  from  the  second,  and  so  on  to  the  last  one. 
Take  the  mean  of  these  results  and  divide  by  the  number  of 
loops  contained.  Th;3  should  give  a  good  niean  value  for  a 
Lalf  wave-length  of  the  vibrating  air  in  the  tube. 

Calculate  the  velocity  in  the  material  of  the  rod  by  for- 
nuila  (1),  having  substituted  the  velocity  in  air  corrected  by 
formula  (2)  for  the  temperature  of  tlie  room. 

The  velocity  in  dry  aiv  at  0°  C.  may  be  taken  as  33250  cm. 
per  second. 

The  temperature  of  the  air  may  be  obtained  witli  suffi 
cient  accuracy  from  a  thermometer  on  the  table  near  the  tube. 
Take  ob.orvations  for  both  the  glass  and  brass  rods. 
Example — Enter  results  thus : 

Temperature  of  air 16.4°  V 

Hence  v^  =  33250  /l. 060024. 

=  34230  cm.  per  sec. 


SOU^D. 


27 


No.  of 
Node. 

Brass  Rod,  I  =  106  cm. 

Glass  Rod.  I  =  108  cm. 

Distance 
from  fisioii. 

Length  of 

Four 

Loops. 

Between 

N.  ■■ 

Distance 
troin  Piston. 

Lenptli  of 

Hve 

Loops. 

Bft«een 
Nos. 

1 
2 
3 

I 

1        6 

1 

8 

9 

10 

10.5 
21.0 
82.0 
4a.  5 
52.6 
63.0 
73.0 
83.0 





7... 
15  0 

2i:.5 

■JOO 





.... 

42.1 
42  0 
41.0 
40.5 

5aud  1 

6  "    2 

7  "    3 

8  "    4 

37.5 
45  0 
53.0 
60.5 
68.0 
75.5 

37.5 
38.0 
38.0 
38.0 
38.0 

1  and  (! 

2  "    7 

3  "    8 
9    "    4 

10    "    5 



Mean      \ 
length  of  (  41-1, 

37.7 
7.09 

1  loop  = 

^  io,a5 

■y,  (for  glass)  =  -;r-r—  /\  34230  =  487800  cm.  per  sec. 


1',  (for  brass)  = 


108 


I03y 


-  X       *'       =  35620(»   '• 


Blank  to  be  Ji lied  in  hy  student. 
Temperature  of  air 


No.  of 
Node. 

i 

Distance 
from  Piston. 

Lenitth  of     Betwten 

:               Nos. 

Loops.     : 

Distance 
from  Piston. 

Length  of 
Loops. 

Between 

No.-*. 



Mean 
length  of 
1  loop  = 

S8 


LABOliATORT  PHYSICa. 


^i 


10.  TO  DETERMINE  THE  VIBRATION  FREQUENCY  OF  A 
TUNING-FORK  BY  MEANS  OF  A  PENDULUM-CHRON- 
OGRAPH. 

Apparatus  Required — A  Buitable  pendulum;  a  tuning- 
fork;  a  stop-watch;  a  centimeter  scale;  a  set  square;  a 
rubber  hammer;  a  suitable  clamp  and  stand  for  mounting  the 
fork. 

Theory  of  Experiment — If  a  pendulum  be  made  to  swing 
past  a  fork  vibrating  vertically,  the  pendulum  and  the  fork 
being  so  arranged  that  the  vibration  of  the  fork  can  be  traced 
by  means  of  an  attached  bristle  on  a  smoked  glass  surface 
attached  to  the  pendulum,  then  the  path  of  the  point  attached 
to  the  vibrating  fork  wi.l  be  a  sinuous  line  as  ABC,  A  and  0 
marking  the  beginning  and  end  of  the  swing  respectively 
See  Fig.  6.  o       r  /• 


N. 


u 


D 

: 

G 

/ 

^ 

H 

/ 

/ 

Fig.  6. 

If  the  arc  through  which  the  pendulum  swings  be  short 
Its  motion  may  be  regarded  as  a  simple  harmonic  motion 
along  the  line  ^4  C. 


I'^AHH*"^-  '■ 


:^rj,. 


■^/^. 


''-'-■ '!r   f--. 


-^ITK^,. 


fi'iS^^ 


SOUND. 


29 


If  the  time  of  motion  from  /'  to  G,  that  i.--,  from  IJ  to 
J5i',  can  be  found,  u  d  the  number  of  vibrationa  <jf  the  fork 
between  tliese  two  pointe  counted,  then  the  numl;er  of  vibra- 
tions per  second  can  Ije  calculated. 

Let -4 ^/A'C  represent  the  auxiliary  circle.  Take  Z>  and 
E^  two  points  on  the  line  AC,  on  the  same  side  of  the  centre. 
Erect  perpendiculars  DFII  and  EGK.  Join  JI  auI  A' to 
the  centre  of  the  circle.  O. 

Denote  the  angle  I/O  A  by  <p,  AOKhy  0,,  the  porio<Jic 
time  of  the  pendulum  by  P,  AD  by  y,  AE  by  y,,  AC  by  2^, 
the  time  of  motion  from  ^1  to  D  (that  is,  from  ^1  to  F  on  the 
arc,  or  from  A  to  //on  the  circle)  by  t,  the  time  of  motion 
from  A  to  ^by  t,,  the  vibration  frequency  of  the  fork  by  n, 
and  tlie  number  of  vil)ration8  between  /"and  O  by  f. 

Since  P  is  the  periodic  time  of  the  pendulum ,. 


0 


(360  .  (j 


0i  =  — ji— 


Hence 


t,  —  t  = 


y    ■ 

PC0,  -  0) 


360 


.     .     (1) 


f,  —  t  being  the  time  from  E  to  O. 


Now, 
Also, 


n  = 


cos  0  = 


>• 

V  . 

360 

<. -< 

"(0. - 

-  0)P 

OD 

_('^- 

-y) 

^>// 


a 


.      .     (2) 


i 


and 


COS  0.  -  ^^     -       ^      • 


80 


LABOR ArORT  PlITSICS. 


If  «,  y,  y.  be  measured,  0  and  0.  can  l,e  found  fro.a 
the  matlienmtical  tables.  Hence,  n  can  be  calculated  from 
equation  (2). 

Practical  Directions-Smoke  the  surface  of  the  glase  plate  by 
pas.ing.t  rapidly  back  aiidforth  through  the  flame  of  an  oil-lamp 

1  eplace  the  plate  in  the  damp  provided  on  the  pendulum 
tor  tJie  purpose. 

Adjust  the  stop-catches  on  either  side  of  the  pendulum 
BO  that  when  it  is  released  from  the  one  it  swings  aeross  and 
just  catches  on  the  other. 

CJamp  the  fork  whose  rate  is  to  be  determined,  so  that  it 
vibrates  in  a  vertical  plane. 

Adjust  the  fork  and  plate  so  that  the  bristle  of  the  former 
just  touches  the  latter  throughout  its  entire  swin..  When 
the  pendulum  is  held  in  one  catch,  the  bristle  should  touch 
tlie  glass  i>late  near  one  end. 

Eelease  the  pendulum  from  the  stop  so  that  it  swings  past 
the  fork.     The  bristle  will  describe  the  arc  of  a  circle 
_    Bring  the  pendulum  back  to  its  original  position  and  ex. 
cite  the  fork  by  a  blow  from  a  rubber  hammer  (if  it  be  not 
driven  magnetically.) 

Kelease  the  pen.lulum  from  the  stop  again,  and  over  the 
arc  already  described  a  sinuous  curve  will  be  traced. 

To  JimJ  P.-IIaving  obtained  a  record  of  the 'vibrations 
of  the  fork,  without  altering  the  adjustments  of  the  pendulum 
set  It  swinging,  and  take  carefully  to  the  fifth  of  a  second  the 
time  of  100  swings;  that  is,  50  complete  oscillations.  F-om 
this  observation  calculate  P. 

To  fvd  0  and  0,-Take  out  the  plate  of  glass.     Care- 
fully join  the  extreme  points  of  the  arc   by  a  straight  line 
At   rwo    points  (as  D  and  E  in    Fig.    (5)  in    fhis    line    bv 
means  of  a  sot  s.)uare,  erect  perpendiculars.  '     ^ 

Measure  carefully,  hy  means  of  a  pair  of  divider'^  and 


mm^^mi^.m 


HOUND. 


31 


luilliineter  scale,  the  lengths  corresponding  to  y,  y„  and  2tf. 
Since  the  values  of  0  and  0,  depend  only  on  y,  y„  aud  r-, 
they  can  at  once  be  calculated. 

To  find  V. — Count  carefully  to  the  tenth  of  a  vibration 
the  number  of  vibrations  l)et\veen  the  two  perpendiculars. 

Precautions. — (1)  Be  careful  not  to  break  the  glass  plate 
when  smoking  it ;  it  must  be  moved  rapidly  back  a  id  forth 
to  prevent  uneven  heating. 

(2)  Be  careful  tu  adjust  the  stops  of  the  pendulum  so  that 
the  whole  arc  will  be  on  the  plate,  otherwibe  the  length,  a, 
will  not  represent  the  amplitude  of  vibration. 

Example. — Enter  results  thus: 
Time  of  oO  oscillations,   07.00" 


Therefore 


r 

.'/  = 

//.  = 

'2a  = 


cos  0  = 
C(J3  0,  = 


l.!>4 

7.;} 

14.0 
32.4 
20.4 

8.9 

2.2 

1(^2 
128.7. 


0 
0. 


—  .5t)° 


0' 


■-  82°  48' 


Hence,  n  = 

Blank  to  he  filled  in  hy  diident. 
Time  of  50  oscillations, 
P 

y       = 


2<(        = 

cos  0    = 


0  = 


cos  0, 


0.   = 


/;  -.i-v-- 


LIGHT. 


II.  TO  COMPARE  THE  INTEWSITIES  OF  TWO  SOIlprpc 
OF  UGHT.    BlraSEN-S  PHOTOMEraR  ^ 

Bea!!''r  nr  rdT' ■'•  '"•   Kn°".l>.2«;  I.a«,i„,.  „„,, 
"■•  !'■  117,  Antliony  an.l  Bn«ikeM,  p.  447;  Barker  ,>   3S, 

be  illuMiinatcl  fro,,,  l,ol,i,„l   ,1, i'      .  ""'or  I,a,„l,  it 

n  ii,  iiiLitrore,  the  two  sources  of  Uo-l.*  +^  v. 

pare,   be  placed  „„e  „„  eaeh  side  of  tbo  V^L  1 ,  '  li^  •"'"" 

^.  tbe  direetio.,  o[.„e  pa;::r  l^r  Zr^  "^"" 

ga.a.-,.t  „„„  „„  p,,„  „f  „„„  „,„„,;, «.»;:,  ^:^- "- 

33 


f 

I: 
t 
i 

4 


^i^^msMM. 


LK.UT. 


33 


A  substitute  for  the  gi'eH>e-.sj)<)t  may  l)e  made  as  follows: 

Take  two  rectaii<j;ular  hlocks  of  parattiiie  wax  of  0(|Uh1 
dimensions.  Between  two  convspuriding  faces  place  a  >tri|) 
of  tin-foil,  adjusting  so  tliiit  two  other  faces  are  in  the  same 
plane.  Place  the  comljinatiun  between  tlie  sources  of  light  so 
that  the  lights  fall  perpendicular  to  the  surfaces  parallel  to  the 
foil.  Adjust  until  the  two  faces  in  tlie  same  plane  are  the 
same  shade. 

liecord  the  observations  of  di>tauce>  /■  and  /•'. 

Iwcpeat  the  observations  for  thi'ce  positions  of  tlie  lamj), 
filament  side  on,  filament  vil^iv  on,  filament  end  on. 

Uei)eat  the  observations  again  with  the  lamj)  and  candle 
75  cm.  apart,  and  again  100  cm.  apart. 

Example. — Enter  results  thus: 


Distance 

Position  of  Lump 

between  Lnriip 
and  Candle. 

I-.  (Lamp.) 

)•,.  (Candle.) 

/,  /,  -  .'  . ,'. 

Filuineiit  side  on 

00 

89.7 

10.3 

14.9  (1) 

"         edfie  " 

;^,8.o 

12. 

10.1  (2) 

end    " 

34.9 

15.1 

5.3  {3) 

side   " 

75 

r.9.r, 

15.5 

14.7  U) 

edge'- 

57.0 

18.0 

9.9  (2) 

end    " 

52.2 

22. S 

5.2  (3) 

side    " 

lUO 

79.2 

20.8 

14.5  (1) 

edjie  " 

76.1 

23.9 

10.2  (2) 

end    " 

69.9 

30  1 

5.5  (3) 

Blank  to  he  Jillal  in  h>j  atiuJent. 


Position  of  Lamp. 


DistHnoe 

bet\ve:'ij  Lamp 

and  Candle. 


)•.  (Ijimp.) 


,  (Candle.)       ///;  =  c'/r,'. 


I  f 


f      : 


34 


LA  nouA  ruit  y  riii\sjv\ 


12.   TO  COMPARE  THE  INTENSITIES  OF   TWO  SOURCES 
OF  LIGHT.     RUMFORD'S  PHOTOMETER. 

References.— Tlie  siime  references  as  in  previous  case. 

Apparatus  Required.— A  Uiiniford  i)hotoniete.' ;  a  wax 
candle;  an  electric  lamp. 

Theory  of  Experiment.— The  intensity  of  illuminavion  on  a 
given  surface  produced  by  a  source  of  light  is  inversely  as 
tlie  square  of  the  distance  from  the  source  of  light,  and  .lirectlv 
as  the  cosine  of  the  angle  which  tiie  huninous  rays  make  witli 
tl»e  normal  to  the  illuminated  surface. 

If  the  two  sources  of  light  be  placed  in  front  of  an  upright 
rod  behind  whicli  is  a  screen,  each  nill  project  on  the  screen 
a  shadow  of  the  rod. 

By  altering  the  relative  position  of  the  two  sources  of  I'ght 
the  intensities  of  the  two  shadows  may  be  made  the  same. 
Then,  since  the  shadow  of  each  is  illuminated  by  the  oth-?r, 
the  illumination  of  the  screen  due  to  each  light  is  the  same. 
Suppose  /  to  be  the  intensity  of  the  one  source  of  light,  ?•  its 
distance  from  the  screen,  a  the  angle  which  the  directioyi 
of  the  l)eam  makes  with  the  normal  to  the  screen ;  then  the 
illumination  due  to  this  source  is  equal  to 

/cos  a 


V 


If  /,,  a,,  /•,  be  corresponding  values  for  the  second  source, 
then  this  illumination  is  efpial  to 


/,  cos  ff, 


i 


iHiK:^c^^Sd:^i»^^fiiiAi^£'^^ 


LIGHT. 


35 


iiiid  fiiice  tlioc  are  equal,  we  liave 

/  cos  a        /,  cos  a 


<»r 


r' 

'".' 

I 

i\  cu.s  n-, 

/,  ~ 

/•,'  CO.S  rt 

(I 


(^) 


\l  a  —  <r,,  tliat  i-,  if  the  directions  of  tlie  luniiiious  rays  be 
eiiiiiilly  inclined  to  the  surface, 


/ 

7. 


(3) 


Practical  Directions. — Attach  the  candle  and  lamp  to  the 
slidiui,'  attachments  provideil  for  the  imrpose. 
f  Adjust  the   angle   Ijetween  the  soi.'res  of  light  until  the 

§        edges  of  the  shadows  just  meet. 

Adjust  the  screen  so  that  the  normal  to  its  surface,  through 
the  rod,  l)isects  the  angle  between  the  directions  of  the  two 
luminous  beams. 

Adjust  the  distances  from  the  screen  until  the  shadows  are 
equally  illuminated. 

This  last  may  be  rather  ditiicidt  to  determine  owing  to  the 
fact  that  the  two  sources,  being  different,  emit  differently 
colored  rays  in  different  proportions,  so  that  the  colors  of 
the  shadows  are  not  (piite  the  same.  In  that  case  the  student 
must  use  his  judgment  as  to  the  equal  densities  )f  the  shadows. 
Measure  the  distances  of  the  candle  and  the  lamp  from  the 
screen.  /',  and  /■„. 

Make  the  comparison  with  the  filament  of  the  lamp  first 
parallel  to  tlie  screen,  then  at  right  angles,  and  finally  with 
the  lani})  end  on.  In  all  three  cases  repeat  the  observations 
for  three  different  positions  of  the  candle  and  lamp. 


il 


msk. 


I; 


3^  LiliOHATOliY  I'UYSWa. 

Example.— Enter  results  thus : 


Pimltloti  uf  Lamp. 


.',  I ,»  =  |/l^. 


^Mlanient  side  on 

38.7 

( ( 

«'llfre  " 

88. 0 

tt 

end    " 

34.9 

Hide   " 

5»..-. 

edge  " 

57.0 

end    •• 

52.  a 

'  • 

aide   " 

79.2 

4  ( 

edffp  " 

7(5.1 

** 

end    " 

79.9 

10. a 

12.0 
15.1 
15.5 
18.0 
22.8 
20.8 
23.9 

ao.i 


14.9 

10.1 

5.:{ 
14.1 

9.9 

5.2 
14.5 
10.2 

5.5 


Blank  to  hejilh'il  in  by  afudtnf. 


I«      ! 


13.  TO  VERIFY  THE  LAW  OF   REFLECTION. 

References. -Knott,  p.  252;    Xiehols  and  Franklin,  vol 
m.   i>.   225;   Carhart,  pt.  i.  p.  211;   Jones,  p.  137;   Hast- 
ings and    Beach,    p.    611;    An.o.s    p.    405;    Anthony   and 
Brackett.  p.  405;   ^^^atson,  p.  44f!:   Barker,  p.  406.    ^ 

Apparatus  Required. -A  di-awinnr-board;  a  piece  of  sil- 
vered  glass  about  10  cm.  long  and  1  cm.  wide;  a  clip  for  hold 
mg  the  glass  in  a  vertical  plane;  half  a  dozen  pins 


III  ■!  I  I    mil     III     III  II II    IIMI      IIIIMi     I  "III 


SlikliA  JMI^Miii^^^illiiii^  •.>•  1.^-  X* 


i 


Lium. 


87 


Theory  of  Experiment.— If  u  plutic  minor  l)e  lieM  in  a 
vertical  plane  and  a  liiiuitious  point  plawtl  in  from  of  it,  an 
imago  will  be  ^een  formed  heliind  tlie  mirror,  no  matter  from 
what  point  of  the  mirror  it  may  U;  reflected. 


Fio.  7. 


Let  A  he  a  luminous  point. 

Suppose  it  to  he  reflected  successively  from  the  points 
a,  />,  E^  F,  on  the  mirror. 

If  the  lines  Zr,  MJ),  XI:,  OF,  he  drawn  markinjr  the 
directions  in  which  the  image  is  seen  from  the  successive 
points,  it  will  be  found  that  they  all  ])ass  throuj;!.  a  point  be- 
hind the  mirror,  the  point  where  the  image  is  seen. 

Denote  this  point  by  B. 

If  A  B  ho  joined,  then  by  measurement  it  will  be  found 
that  AJfis  equal  to  MB,  and  that  A  B  is  perpendicular  to  FM. 

From  this  it  follows,  obviously,  that  the  angle  of  incidence 
is  equal  to  the  angle  of  reHcction  ;  e.g.,  the  angle  PFA  is 
equal  to  the  angle  PFO,  where  PF  is  "perpendicular  to  FM. 


38 


LA/iOUA  ion  Y  I'll  YSK  S. 


Practical  Directions.— (1)  iMistun  u  >ln..it  cf  i-uU.I  foolsmp 
pajwr  \x\x}\\  a  drii\viii^'-lH.Hrtl.  Stick  ii  iiniiil.fr  of  pins  vciti- 
cally  into  the  hoard  aloni;  tjjio  ol"  the  liruH  of  the  paptr. 

Let  these  l)e  represented  by  the  points  /•',  h\  />,  t\  in  the 
preceding  diagram. 

Place  the  mirror  in  tlie  winie  vertical  |»Iane,  with  its  sil- 
vered face  tonching  the  pins,  and  adjust  it  so  that  i^s  edges 
are  parallel  with  the  paper,  the  lower  edge  being  about  one 
centinu'ter  above  it. 

Stick  another  pin,  also  vertically,  at  a  point  corresjMnid- 
ing  to  .1  in  the  diagram. 

lierieet  this  pin  successively  from  the  points  (\  />,  h\  F. 
Thi>  can  be  done  by  getting  the  image  of  the  pin  at  A  in  a 
line  with  the  pin  at  each  of  the  points,  and  marking  the  direc- 
tion in  eacli  case  by  means  of  pins  at  /.,  J/,   .\'.  <P. 

Now  remove  the  mirror,  and  join  L<\  Ml),  \ h\  and 
OF,  producing  them  to  meet.  The  .>^ame  j.in  will  do  for 
marking  the  \)o\\\U  Z,  M\  N,  ().  If  the  obse-vntions  are 
carefully  taken,  the  lines  Z6\  J//-»,  X K,  and  (>Fw\\\  meet  in 
a  ))oint.     To  show  tlie  results,  draw  the  complete  diairmm. 

(2)  It  follows  geometrically  that  if  the  angle  of  incidence 
be  ecpial  to  the  angle  of  reflection,  the  position  of  the  ima«re  is 
liehind  the  mirror  at  a  distance  e(]ual  to  the  distance  the  object 
is  in  front,  and  that  the  line  joining  the  object  and  imai:-e  is 
perpendicular  to  the  mirror. 

Hence  the  law  of  reflection  can  be  verified  exi)erinieiitally 
by  n)easuring  these  distances. 

Place  the  mirror  as  I)efore  in  a  vertical  j.lane  so  that  the 
lower  edge  is  about  a  centinjeter  above  the  pa])er. 

Stick  a  pin  vertically  at  a  distance  of  ](»  to  15  cm.  in 
front  of  the  mirror. 

Xow  M-hile  observing  the  image  of  the  jnn  behind  the 
mirror,  stick  another  pin  so  as  to  coincide  with   this  insa-'e. 


LIGUT. 


;j!> 


In  order  to  deteriiune  wliether  the  two  rcully  coiut'i..e,  uiove 
the  eye  at  riglit  uiiglca,  hack  and  forth,  to  the  direction  of  the 
two  pirirt.  If  the  second  pin  coinciden  with  the  image,  the 
two  will  appear  to  move  together,  otherwise  they  will  appear 
to  move  away    rom  each  other. 

Having  adjusted  tlie  pin  to  a  proper  position,  measure  tlif 
distances  of  the  two  pins  from  tlie  silvered  side  of  the  mirrtr, 
and  verify  with  a  set-scjuare  the  j)eri)endicularity  in  each  case. 

The  small  differences  may  l)e  due  to  tiie  unevenness  of  the 
glass,  or  to  faulty  observations. 

Take  at  least  six  readings. 

Example. — Enter  results  thus : 

(I)  Show  complete  tliugrum. 

{'!)  Show  diagram  an<l  tahle. 


Dl»t.  of  IMii  from  Mirror. 


10  cm. 

la.i " 

15     " 
17.2  " 


DIM.  of  IiiinK**  l>'bitid. 


10.2 
112 
15.2 

17 


nifferfncf. 


.2 
.1 
.2 
.2 


Blank  to  hf  jiUed  In  hij  utmh  nt. 


DiHt.  of  Pin  from  Mirror.  Hint,  of  ImaK*- b«'liind. 


|iiff<MVIlff. 


40 


LAnohAroRY  physics. 


I 
I   p 

*. 
i 


!    I 


^! 


14.  TO  FIND  THE  ANGLE  OF  A  PRtsM.     P.^N  METHOD. 

o^a^tT?'"^^^'*'""''  J"-  ^^^'   ^^^'^''^  ^  ■•3<';  Knott,  p. 
J63;  Nichols  an,l  Franklin,  vol.  in.  p.  38;  A.nes,  p.  429 

Apparatus  Required.- A  prism;  a  pair  of  dividers;'  a 
centimeter  scale;  a  book  of  lojraritliinic  tahles 

Theory  of  Ex^riment. -Suppose  from  a'  luminous  point 
A  a  ray  ot  light  fall  upon  the  edge  of  a  prism  POq\  and 


t  at      :s  refl  eted  from  the  s,de  OQ  ,t  the  edge  O  along  the 

i  ce  tho        .      ;•"•'      r  "'^'  ''^'^^'"'^^  ^''^'  '"-'  ^  ^^-     Then, 
since  the  ungle  ot  mcidence  is  ecp.al  to  the  angle  of  reflection 


and 


AOy^  FOB, 


KG  heing  perpendicular  to  PO^  and  FO  to  QQ 

If  AG  bo  produced  to  />,  it  is  evi<lent  geometrically  that 


LIOHT. 


41 


the  anglo  COP  is  eqnal  to  the  angle  POD,  H?id  that  tlie  angle 
BOQ  is  equal  to  tlie  angle  DOQ. 

Tlierefore  COB  is  double  POQ,  that  is,  double  the  angle 
of  the  prism.  Hence  if  COIi  be  measured,  the  angle  of  the 
l)rism  is  found. 

Practical  Directions.— Describe  a  circle  with  a  radius  of 
.0  cm.,  centre  C.  Place  the  prism  with  the  angle  to  be 
found  at  the  centre  of  the  circle.     Stick  a  pin  vertically  at  a 


Fio.  9. 

int  A  on  the  circumference,  so  that  the  line  ^T  approxi- 
mately bisects  the  angle  of  the  prism. 

Mark  the  direction  of  the  retlection  of  the  pin  A  by  stick- 
ing a  pin  at  E,  so  that  //,  the  image  of  A,  and  the  edge  C 
are  in  a  straight  line. 

IVfark  the  point  B  in  the  same  wav. 

A'ow  liCE'i^  equal  to  twice  LCM. 

If  BtJhe  bisected  at  /rand  joined  to  C,  then  CVf  bisects 
lU'K,  and  also  is  perpendicular  to  Bh\ 


: 


f  XT. 

if 

'I 
t   f 


it 


15.     . 


*2  LABOR  A 1 0 1:  Y  PHYSICS. 

Hence  the  angle  lit'K  u  equal  to  the  angle  LCM. 


Now. 


BV      2nC' 


Hence  measure  BE,  divide  hy  twice  BC,  and  the  result 
is  the  sine  of  the  angle  LCM. 

By  reference  to  the  table  of  natural  sines  the  angle  nmy 
be  four  j. 

Measure  the  three  angles  of  the  prism. 
Example — Enter  results  thus : 

RADIUS  OF  CIRCLE  10  CM. 


Angle. 

BE 

.Sin  /. 

i 

/. 

1st  augle 
2(1  angle 
3d  augle 

17.33 
17.40 
17.20 

1 

.8665 

.870 

.860 

60'     3- 
60    30 
59    34 

Sum  of  ang 

les  of  jirisni 

Difference  f 

rom  180* 

*l' 

Blank  to  he  fill 

'd  in  hy  fttudeti 

t. 

Angle. 

BE 

m 

Sill  /. 

I. 

1st 
2d 
3d 

Sum  of  anpl 

t*8  of  prism 

Difference  fi 

rom  180* 

. 

- 



^^^mi^^ 


Lionr. 


43 


15.  TO  FIND  THE  REFRACTIVE  INDEX  OF  GLASS. 

References — Uarker,  p.  424;  Watson,  p.  4«)8;  Carhart, 
p.  257;  Ames,  p.  42Ji;  Nicliols  *fe  Franklin,  vol.  iii.  j).  3(5: 
Knott,  p,  259;  Hastings  and  Beach,  p.  615;  Anthonj  an  • 
IJrackett,  p.  407. 

Apparatus  Required.— A  glass  plate;  a  drawing- 1  )oar(l ;  a 
sheet  of  white  paper ;  a  few  pins ;  a  centimeter  scale ;  a  set- 
6<|uare. 

Theory  of  Experiment — If  a  ray  of  light  f'F  fall  upon  a 
plate  of  glass  ABCJJ,  then  on   pa.*sing  into  the  glass  it  is 

L 


bent  along  a  line  FG,  making  the  angle  GFKMvhh  the  nor- 
mal /,/%  less  than  the  angle  LFE.     The  ratio 

sin   Z/7i^ 
sin   (^FK 

is  called  the  refractive  index  of  the  glass. 

Denoting  the  refractive  iiidex  of  glass  by  ;<,  the  angle 
LFKhy  0,  and  tiie  angle  f,'F/ih\  0,, 


M 


sin   0 
sill   0,' 


■i^i^^Km^iy^^^mmi^iimm:!^]^:*:^^^!^^?:^ 


44 


LABORArORT  PJIFSICS. 


I 

I- 
i, 


If  0  and  0,  be  deterniined,  /<  cati  be  calculated 
Practical  Directions—Fasten   u   sheet  of   paper   on   the 
draunig-board,  and  on  it  pluce  the  square  of  glass  plate. 
The  glass  should  be  at  least  J  of  an  inch  thick. 
Stick  two  pins,  J^-md  K.  vertically  into  the  board  so  that 


Pio.  11. 

the  line  joining  them  makes  an  angle  of  abo-it  30°  with  one 
c(]ge  of  the  plate. 

Now  look  through  the  opposite  face  of  the  plate,  and  the 
refracted  unages  of  the  two  pins  can  be  seen. 

Adjust  the  positi..n  of  the  eye  till  the  two  images  appear 
m  a  straight  line. 

Mark  the  direction  of  this  line  by  sticking  two  other  pins, 
^  and  //,  so  that  these  two  an.l  the  refracted  images  of  the 
other  two  are  in  one  straight  line. 

Mark  the  position  ..f  tl.e  glass  on  the  paper,  and  remove 


#;:£ 


IIM^ 


mi^. 


LIGHT. 


45 


Join  FE,  and  jiroduce  to  cut  the  line  wliicli  marks  the 
edge  AB  of  the  glass  in  L. 

Join  Gil,  and  produce  to  meet  the  edge  CI)  of  the  glass 
in  K. 

Join  LK.  Then  the  ray  of  light  falling  on  the  glass 
at  /,  along  the  line  EI\  is  refracted  through  the  glass  along 
the  line  AT/,  and  emerges  along  the  line  (J II. 

Measure  off  /./;,  lo  em.,  and  h\  means  of  a  set-square 
erect  a  perpendicular  from  ^'on  the  normal  MFM\. 


Then 


sin  0 


EM 

JO  • 


Produce  if  necessary  LK  to  /s',  till  LE,  is  10  cm.  long, 
and  erect  a  perpendicular  K,  JA,  on  MEM,. 

E,JI, 
Measure  ^W^and  E,M,. 


_  EM 

^  ~  e,m: 


Repeat  the  observations  for  three  different  values  of  0. 
Example. — Enter  results  thus: 


EM. 

F,.V,. 

M- 

5.67 
6.47 
9.08 

3.72 
4.26 
6.01 

1  51 
1.52 
'  51 

Mean  value 

1.515 

, 

^^WWl: 


46 


LAliOhWroliY  I'lliSICS. 
Show  (•oin])Iete  (liii^'nim  in  v;w\\  case. 

JiluHk-  to  hf  p'lh'il  hi  h»i  ximh'iit 


KM. 


Mean  value  of  n . 


■!«=>• 


i  : 


f    i 


I 


16.  (I)  TO  VERIFY  THE  LAW  THAT  WHEN  A  RAY  OP 
LIGHT  IS  REFRACTED  THROUGH  A  PrYsM  THE 
ANGLE  OF  INCIDENCE  PLUS  THE  ANGLE  OF 
EMERGENCE  IS  EQUAL  TO  THE  DEVIATION  PlSs 
THE  ANGLE  OF  THE  PRISM.  ^'^^^"'^  ^^^^ 

(II)  TO  FIND  THE  REFRACTIVE  INDEX  OF  THE  PRisM. 

"■'<!  I>^arl,,  J.,  hh  :  k,u)tt,  ,,.  26;^;  Ames,  p   42{» 

Apparatus  Required.- A   prism;    a  pair  of   dividers-    a 
cr.mmeUM-  sc-ale:  throe  pins:   a  set-square 

p n.Mu  ABC    Hg.  12)  from  a  himinous  point  />,  at  the  point 
C>.  and   bo  bent  through   the  prisn.  alon.  a  <1  root    n    Z 
eniergincr  ah.ntr  /^S    POD  w  fl.o         i       r      '^^*^"*"    v^*^' 
/'/?s"thr  .nurl      f  ^  ^  '''"^''^  '^^  i-.eidenco.   and 

Vt/i-.S  the  an.irle  of  emerc^ence,  where  DQ  and  /f7?  are  perpen- 
dicular respe<.tivelv  t..  J /,>  ;,nd     16^  *    ^ 

Denote    PQU   I.v  0.  /,V>V  I,,-  ,;,  j^^.^f.  ,^^.    ^ 
^^v..     ^-c/>^and^Xn.etin/:..^,,^:;:;l,^^^ 


and 


Fk;.   12. 


QFS  =  1  80  _  rf 


QGR=  ISO-  /, 
FQ(;  =  0, 

Hence       1  N(,°  __  /  +  i  s,, .  _  rf  +  0  +  ,/.  =,  g^jo", 
ami  therefore  0  ^  ,^.  ^  <y  ^  / 

If  tl.e  incident  ray  fall  m  that  QH  is   parallel  to  BC 
tiien  0  ^  ,^.^ 


and  in  that  case    20  =  d  -f-  y,     or     0 
Kow  if  /<  be  the  refraction  index  of  tl 


^-\-  f 


9 


lie  prism, 


_       sin  0 


sin  0 


sin  JiQG      sin  0, 
When  0  zz.  ,/.,    /.>^^  ^  Qji^^    ,,j.  ^^  ^  ^^, 


N 


ow  since  0,  +  ,/-,  +  is,)  _  ;  ^  j,s„o^  ^j^^^.^^ 


ore 


20,  =  /,     or     (A.  = 


/ 


48 


LAliOllATOHY  PUY8IC8. 


Hence 


sin 


/*  = 


2 


mx- 


(2) 


It  may  be  sl.own  geometrically  that  when  0  =  ^.,  the  de- 
viation, d,  is  a  niinimuiii. 

Practical  Directions.-(I)  Describe  a  circle  with  a  radius 
of  10  cm.,  Fig.  i;{. 

Phu-e  the  prism  with  it.  edge  at  .4,  the  centre  of  the 
circ  e.  Stick  a  pin  vertically  at  a  point  1\  such  that  the 
angle  which  /'./  makes  with  the  face  AB  is  less  than  a  ri.rht 
angle.  Observe  the  direction  of  the  refracted  image  alo'nir 
the  line  AR.  ^ 

Stick  a  pin  at  R,  in  such  a  position  that  the  image  of  the 
pm  at  P  is  in  a  line  with  the  c^h^a  of  the  prism  and  Ji. 

Draw  JJA  pi ri)endicular  to  the  face  AB,  and   EA  per 
pendic-nlnr  to  the  face  A  C.     Join  PA  and  liA,  and  produce 
I*A  till  It  cuts  the  circle  in  F. 


Then 


PAD  =  0, 
AAP  =  y,, 
FAIi  =  6. 


Draw  PO  perpendicular  to  J) A,  FiV  and  FMto  Ali 

Then, 

hN 


sm  if)  =  — , 


t^iii  '/'  - 


pin  <^ 


FM 


where  /•  is  the  radill^  .:,f  t-he  cirele. 


LIGHr. 


49 


Measure  PO,  EX,  FM,  and  calculate  the  values  of  and 
0,  ^,  and  6  ttoin  the  sines. 


Fig.  13. 

periment  ll/'  '^'"  '"^^'  '^  ''"  P"''"'  ^^  *^'^  "^^^^'^^  ^^  E- 
Substitute  the  values  in  formula  (1). 

this^IuL^.r'  ''^■'""'*  ^"'  "'""'""•"  ^^^•^^^•^"-     To  aecon^plish 

axis  and  observe  whether  the  deviation  increases  or  decreases 
by  obsernn.  whether  the  direction,  AI,,  of  the  refracted  ra" 
make,  a  larger  or  smaller  angle  with  the  direction,  JF  of 

wher      I        v"  ,'■"'""  ^   ''  ""^'  reverse  the  process, 
tion,  the  angle  will  decrease. 

/^/i.!rn^'"'''''-^'  ""'"'""''  '^"''^  ^'«  found  that  angle 
r^Vli  reaches  a  minimnin  viln,.  ....  '  *i       •  ^^ 

which  U-.V  fl        ".""":'"'"  ^'>l>'^*  '"H.  then  mcreases  no  matter 
^Uiich  \\A^  the  ^rism  is  turned. 


50 


?: 


LAIiORATORT  PHYSIVS. 


Adjust  for  the  exact  position  of  „a«i,n„,„  deviation  and 
measure  6  as  before. 

Calculate  /i  from  formula  (2). 
Example — Enter  results  thus: 
Show  complete  diagram  in  each  case. 


I. 


^'Q   =7.r 

Hii  0=  .77^ 

h\V  =  9.85 
An  tf}  =  .j)>io. 
JfF  =  \)A2 
m\S  ~.  .042, 


0  =  50°  24' 
tf)  =  80°  00' 


<J  =  70°  24' 
/  =  60"^  00' 
V^  -r  y^  ••-  130'  30' 
<y+  /  =^30°  24' 
Ditference  6' 


II. 

F2V  =6.18 

sin  d  =z  .r,lH 
6  —  38°  12' 


sui 


A*  = 


2 


sin  -7 


/ 

2 

_  sin  49"  6' 
~"  8in~30°~ 
=  1.51 


^Q    = 

sin  0  =r 

z;:y  = 

t>iii  1^'  = 
J//'  = 
sin  6  = 


i^/aw^-  <o  Ag///e</  in  hy  student. 


0+  V^'=r 
rf+   /  = 

Difference 


0  = 

V'  = 

rf  = 
/  = 


sin  6  = 


I.10IIT. 


tl 


"'■a™sohS,''«™1.''*""'*    "^   CURVATURE    OF 

ItlMI      ililllKllll       V(»         III       i>      "•)  .        \  .  »I  1      .. 

>   ^<".   III.  ]..  .,2,    A.:tli(>nv  and  I'.rackftf.  u    s- 
'"i'-l<'''S  !••  41!>;    (Wlmrt,   |.t.   ,,  j,    >>J.,  '        ' 

Apparatus  Required.- A  .pLercueter ;  u  sp|.ori<.al  M„face • 

Theory  of  Experiment.  -Tl,.  .|,la.,-„,„.t,.r  ,.,„«i..„  „f  „ 

of  tho  colh,-  ,.,  «l,i,.l,  ,|„  ,,,„  „„  a,„u.l,e,l  L  tin..  ,s,"  „ 
«.rO,ns  „  g™|„„,e,l  ,|i,k,  «l,icl,  moves  ,,„i,e  near  „  ,-,  .  ■ 
a.o,I  n,„.^-,,t  ...lo  „,t„el,e.l  ,„  „„e  of  „,o',e«».  ',•::;; 
...ent  ,«  hrst  so.  „„  a  plane  gl„»  „„.f»ee  and  «,e  een.re  "  ew 
turned  dl  the  ,K,int  jn.t  ,„nehe»  tl,e  surface  of  „,e  ,L  It 
..  then  ,mnsferre,l  to  the  spherieai  snrfaee,  a„.i  L  c  ntre 
«.•".»•  turned  nntil  it  ,«ain  tonehes  the  snrfaJe.  If  ,  ',"2 
.l.m.™,ee  „f  the  two  readinf-s.  and  /  (he  .listance  hetween  the 
Icff.  ot  the  s|,l,eron,eter,  th,.,  the  radins  of  the  spherieal  s,,r. 
jaee  is  given  by  the  equation 


• 


This  may  ho  sliowii  thus; 

I.et  AIi/)C  he  the-  sph.Mical  surface  (Fi-.  U),  a„d  D 
the  po.nt  „,u.,,  the  sereu-  of  rhe  sphero.uete.-  touches  the 
surface  ul.eu  the  three  h>jrs  are  aI>o  touchin.^  it 

Then  .1//  is  tlH-  .iian.eter  of  the  circle  passin.  ti.rouHi 
three  points  wJiere  the  legs  rest  on  tlie  surface. 


i4 


H 


J.A  uoiiA  roH  Y  j'li  rsics. 


If  these  tliree  poiiitH  bo  joined  on  the  ]>lune  of  tuu  circle, 
an  eciuilftteral  triangle  wonld  be  formed.  • 

Denoting  the  distance  between  the  legs  by  /,  we  have 
geometrically 

where  a  is  the  radium  of  the  Rniall  circle. 


Now 


(2/'  -  6)6  =  a\ 


(2) 


Bii:ce  D/i(yh  a  semicircle,  where  6  is  tlie  distance  from  flie 
point  U  on  the  snrface  to   the  plane  of   the  feet   of   the 


i 


1 


^^pherometer,  that  in,  the  <listaiice  throui;h  which  the  ])uiiit 
nuist  be  inuveu  from  its  iii'st  tu  ir>  second  po»itiun. 


k^lJL 


UtiBT.  68 

Hence,  combining  (1)  and  (2)  and  solving  for  /•,  we  get 


(3) 


Practical  Directions. — Tlio  ecivw  of  the  Hplieroinetor  hat 
UHually  a  pitch  of  ^  mm.,  and  the  upright  scale  is  similarly 
divided. 

The  graduated  disk  is  also  divided  so  as  to  give  exact 
fractions  of  a  turn. 

I'lace  the  spherometer  on  the  plane  glass  surface  provided 
for  the  purpose,  and  turn  the  iscrtw  until  it  just  toJichcs  the 
surface  of  the  glass. 

Read  the  u})right  scale  and  also  tht  disk. 

Place  the  spherometer  upon  the  spherical  surface  and 
turn  the  screw  until  it  again  just  touches  the  surface. 

Read  the  upright  scale  and  the  disk. 

If  the  graduated  disk  he  divided  into  lOu  ]>arts,  divide 
its  reading  by  2,  aisd  add  to  the  reading,  expressed  in  milli- 
meters, of  the  upright  scale. 

If,  however,  the  graduated  disk  be  <livided  into  Tm)  j)arts, 
add  at  once  the  reading  as  the  decimal  of  a  millimeter. 

The  difference  between  the  first  and  second  readings  gives 
the  value  of  <S. 

As  the  value  of  S  is  very  small,  great  care  must  be  taken 
with  the  observations  in  order  to  secure  accuracy. 

Take  at  least  six  rcaditi;rs  in  each  case. 

Express  the  mean  ditferejice  in  ceritimeters. 

Measure  the  distance  between  the  legs  in  centimeters  and 
substirute  in  the  formula. 


}  i 


lii 


,*f 


if 


■j 


W  LABORATOBY  PHYSICS. 

Example — Enter  results  thus : 


KeadiiiK  on 
i^l'liei'iciil 
Surface. 


10.28 
10.23 
10.24 
10.22 
10.23 
10.24 


Meau  value , 


Blank  to  he  Jilhd  in  lnj  student. 


Reading  nti 
Plane  Surface. 

K<>a(liii|;  on 
Hpherical 
Surface. 

1 

i  (mm.) 

/  (cm  ) 

1 

'■  (em.) 

Menu  val 

ue 

" 

'  ■  ! 


I     I 


i8.  TO   DETERMINE   THE   RADIUS  OF   CURVATURE   OF 
A  CONCAVE  MIRROR  BY   REFLECTION. 

References.-K'.mtt,  pt.    ■,.    ,,.  2:,0;   Ni<.l„.I.s  and  Frank- 
lin, vol.    in.   p.   .•?!>:    Ames,    p.   413:    IIa..tinirs  and   iJeael, 
p.   613:    Antlumv  an.l   Tirackett,    p.   40S :   AVatson,  p.  459  • 
Barker,  p.  419;   Carhart,  pt.  i.  p.  249, 


uonr. 


Apparatus  Required.— A  concave  mirror;  a  cli|>-staiKl ;  a 
piu  ;  a  centiincter  scale ;  a  sphL-rometer. 

Theory  of  Experiment.— If  an  object  be  held  in  front  of  a 
concave  mirror  beyond  its  geometrical  centre,  an  inverted 


Fi<>.  15. 

image  of  tbe  object  will  l)e  seen  between  the  object  and  the 
nnrror. 

Thus  if  the  obje  be  held  at  A  (Fig.  15),  and  C  be  the 
geometrical  centre,  the  image  will  be  seen  at  a  point  />,  when 
the  angle  AKC  =  GKD. 

If  now  the  object  be  moved  up  to  the  centre,  6',  the 
direct  and  reflected  rays  will  have  the  same  path  along  (JK. 

The  image  will  therefore  coincide  with  the  object. 

If,  therefore,  the  object  be  so  placed  that  the  image  is 
seen  to  coincide  with  it,  the  distance  of  the  object  from  the 
mirror  is  the  radius  of  the  mirror. 

Since  /,  the  focal  length,  is  equal  to  one-half  the  radius, 
it  can  be  obtained  directly. 

Practical  Directions — Place  a  pin  vertically  in  a  clip  in 
front  of  the  mirror. 

Adjust  its  position  so  that  an  inverted  image  of  the  pin 
can  be  seen  between  the  pin  and  the  mirror. 

Move  the  clip  toward  the  mirror,  and  adjust  until  the 
point  of  the  image  appears  to  coincide  with  the  point  of  the 
liin.  To  determine  the  exact  position  of  coincidence,  let  the 
pin  and  the  image  slightly  overlap  and  then  move  the  eye 


86 


r.A  nouA  TOR  Y  I'j/rsivs. 


back  aiul  forth  so  that  tliey  can  be  seen  from  ditferent  polnb^ 
of  tlie  nurror.  When  the  i>oint  of  exact  coincidence  is  found, 
the  pin  and  nnage  will  continue  to  occupy  the  same  relative 
l)08.t.on  to  each  other,  no  matter  at  what  point  of  the  mirror 
thev  may  be  observed. 

Having  thus  found  the  point,  measure  by  means  of  a 
cenrnneter  scale  the  distance  of  the  pin  from  the  mirror. 

liepeat  the  operation  several  times. 

The  mean  of  the  observations  may  be  taken  as  the  radius. 

Verify  your  results  by  a  spherometer. 

Example — Enter  results  thus : 


Observation. 

r 

Ist 

7123 

8d 

72.31 

8d 

73.25 

4th 

72.20 

Sth 

72.18 

6th 

72.24 

t 

Mean  value 

72.23 

r  by  spherometer 72.3.'} 

Mini-  to  hejilled  In  by  stiulmt. 


Observation. 


Mean  value 


r  by  spherouicter 


tlOHT. 


57 


19.  to  DETERMINE  THE  RADIUS  OF  CURVATURE  OF 
A  CONVEX  MIRROR. 

References. — As  in  Experiment  18. 

Apparatus  Required.— A  convex  mirror,  suitably  mounted; 
two  clamp-stands  holding  small  upright  rods;  a  tape  meat>ure; 
a  centimeter  scale;  a  telescope. 

Theory  of  Experiment. -If  00,0,  (Fig.  16)  be  the  axis 

of  a  convex  mirror,  BB, ;  A  and  A,  two  objects  situated  so 

A 


Fig.  16. 

that  ^^  is  equal  to^,^,  and  AA,  at  right  angles  to  00  C 
and  C,  the  positions  of  the  image  of  A  and  A,  as  seen  in'the 
mirror,  0,  being  the  centre  of  the  spherical  surface;  then 

_1 L_         2 

AB      BC  -  ~  OM'     ••••(!) 

u        V  r ' 

where  w,  v,  and  r  are  resi)ectivelj  equal  to  AB,  BC,  and  0,B. 

nr 


Hence 


V  = 


(2) 


2w  4-  r 

Denote  CC,  by  x,,  AA,  by  x,  and  if.V,  the  intercept 


m^su^v^sar^^^ 


."ift^.-TViS^-stf, 


58 


LABOUAIORY  PHYSICS. 


5i 


OH  the  tangent  to  the  surface  at  O^  made  by  joining  OC  and 
Then  from  similar  triangles  we  liave 


and 


or 


X 

— 

«4 

-  r 

a;. 

/•  — 

■  v' 

3l 

a?. 

= 

(9^>. 

+ 
GO, 

» 

a'. 

«  + 

V 

», 

?< 

» 

(3) 


(4) 


IS 


since,    00,    being   large   as   compared  with   AA,,    00, 
approximately  equal  to  AB. 

Combining  (3)  and  (4),  substitntM.g  for  v  the  value  found 
in  (1),  and  solving  for  /•,  we  obtain 

In  practice  the  distance  00,  may  be  substituted  forw  for 
the  reason  given  above. 

The  measurement  of  MN^  (x,)  requires  the  use  of  a 
telescope. 

Practical  Directions.— Fix  the  mirror  in  the  clamp  pro- 
vided  and  in  an  upright  position. 

Place  the  telescope  at  a  distance  of  two  or  three  meters 
from  the  mirror  and  adjust  its  direction  and  height  until  the 
axis  of  the  telescope  is  in  Hue  with  the  axis  of  the  mirror. 

Place  the  clamp-stands  with  the  upright  rods  in  the  positions 
corresponding  to  A  and  A,  (Fig.  Ifi),  the  line  joining  the.n 
passing  through  the  object-glass  of  the  telescope  and  being  per- 
pendicular to  its  axis.     AA,  should  be  from  40  to  70  cm. 

The  telescope  can  now  be  focussed  on  the  images  of  the 
npright  rods  seen  in  the  mirror. 

To  obtain  the  intercei)t  at  the  snrfaco  of  the  mirror  corre- 
sponding to  i¥iV^or  .«„  fivsten  u  centimeter  scale  across  the 


LIGHT. 


59 


face  of  tlie  mirror  in  a  position  ci^rrespondin*,'  to  />/>,  in  the 
fiirure.  The  upper  edge  of  the  scale  siiouid  approximately 
hi.sect  tlie  mirror. 

By  slightly  altering  the  focus  of  the  telescoi)e  both  the 
scale  and  image  can  [)e  seen  and  the  distance  between  the 
images  as  seen  on  the  scale  observed. 

Head  this  distance,  x  . 

Measure  the  distance,  x,  between  A  and  A^, 

Measui-e  the  distance  between  the  object-glass  of  tlie  tele- 
scope and  the  surface  of  the  mirror,  ?/. 

Substitute  in  formula  (5)  and  calculate  /•. 

llepeat  the  observations,  changing  the  positions  of  the  tele- 
scope and  upright  rods  each  time. 

Verify  your  results  hy  the  spheroiueter. 

Example. — Enter  results  thus : 


Obs<trTation. 


(1) 
(2) 
(3) 


300 
250 
275 


60 

55.5 

48.7 


6.22 
6.65 
5.40 


Mean  value  of  r. 


r  by  spberonieter 

Blank  to  he  filed  In  hy  stiuhni. 


Observations. 


Mean  value  of  r. 


r  iiy  splierometer. 


78.5 
78.7 

78.4 


78.5 
78.6 


60 


LABORATORY  PHYSICS. 


20.  TO  DETERMINE  THE  FOCAL  LENGTH  OF  A  CONVEX 
LENS  BY  PARALLEL  RAYS.    METHOD  I. 

References—Barker,  p.  435;  Watson,  p.  480;  Carhart, 
pt.  I.  p.  273;  Hastings  and  Beach,  p.  619;  Nicliols  and 
Fmnklin,  vol.  iir.  p.  45;  Knott,  pt.  ii.  p.  267;  Ames,  p. 
440;   Antliony  and  Brackett,  p.  412. 

Apparatus  Required.- An  elementary  optical  bench  pro- 
vided  with  ground-glass  screen;  several  convex  lenses;  a 
telescope. 

Theory  of  Experiment. -(«)  if/  be  the  focal  length  of  the 
lens,  u  and  v  the  respective  distances  of  the  object  and  image 
from  the  surface  of  the  lens,  then  we  have,  from  the  law  of 
convex  lenses, 


..  -t-  ^      /■ 


11 


(1) 


If  the  incident  rays  be  parallel, 


—    =  0, 


and  hence 


V  =  /: 


(2) 


It  is  only  necessary,  therefore,  to  observe  v. 

{h)  Another  method  involving  the  same  principle  is  as 
lollows:  If  a  telescope  be  carefully  focussed  on  a  very  distant 
ol)ject,  and  afterwards  it  be  used  to  view  a  near  object  through 
a  convex  lens,  the  distance  between  the  lens  and  the  object  will 
be  equal  to  the  focal  length  of  the  former,  when  a  sharp  image 
of  the  object  is  seen  in  the  telescope. 

For,  only  parallel  rays  will  come  to  focus  in  the  telescope 
and  the  rays  after  traversing  a  lens  from  a  given  object  are 
parallel  when  the  distance  between  lens  and  object  is  equal  to 


'{^»^. 


'^^ 


LIGHT. 


61 


the  focal  length  of  the  lens.  In  this  as  in  the  preceding'  case 
only  one  observation  is  necessary. 

Practical  Directions.-^,)  Select  a  lens  having  a  focal 
length  not  greater  than  the  length  of  the  bench. 

Mount  it  on  its  stand  with  its  axis  along  the  bench. 

Mount  the  groun<l-gIass  .screen  behind  it,  with  the  plane 
of  the  screen  at  riglit  angles  to  the  direction  of  the  bench. 
It  is  important  to  have  the  \^m  and  ground-glass  screen 
occupy  the  same  i)osition  in  relation  to  the  indexes  which  are 
carried  bv  them. 

Point  the  apparatus  to  an  open  window  so  that  an  image 
of  a  distant  object,  such  as  a  church-spire,  may  be  obtained 
on  the  screen. 

Slide  the  lens  along  the  bench  until  a  clearly  defined 
image  of  the  object  is  obtained. 

Read  the  distance  between  the  indexes  carried  by  the 
lens  and  screen. 

This  distance  is  the  focal  length. 

Repeat  the  observation  three  times  for  each  lens  and  take 
the  mean  of  the  results. 

The  image  is  begt  viewed  from  behind  the  screen. 

{h)  Select  an  ordinary  reading  telescope  and  focus  it  out 
of  doors  on  a  very  distant  object. 

Place  the  telescope  on  the  optical  ben  li,  close  up  to  tl,( 
lens  in  question,  so  as  to  look  through  it  ."i  the  direction  of 
the  bench. 

Mount  a  piece  of  white  printed  paper  on  one  of  the  bench- 
stands,  so  that  the  plane  of  the  paper  is  the  Pame  as  that  of 
the  index  carried  by  the  stand. 

Illuminate  the  paper  by  a  strong  light  which  is  shaded 
from  the  lens. 

Move  the  paper  along  the  bench  until  a  clear  image  of  the 
printing  is  seen  in  the  telescope. 


I    I 


•  'T\r  -  -|iiirr  i  -iniTi  if  imm  ~niiiTiB«gn r" '~  ruinr ~T 


62 


LAUOlilTOHY  I'liytiWS. 


Read  the  distance  hetween  the  lens  and  object 

VHh,t^",fV''""  "'''  '■""""^'"'  "''  ^'*'^^"  ^^'-'-  '"-"  f-  the 
Example.— Enter  results  thus: 


I^eiis. 


Method  I 

. 

■ __ 

Metho<l  ft. 

LeDM. 

f. 

Mean  Value 

1 

for/. 

Irf-iit*. 

f. 

1    Mean  Value 



1          for/. 

A 

13.0 

j 

" 

12.2 

A 

12.1 

B 

12.3 
17.2 
17.3 

12.25 

B 

12.0 
12.2 
17.3 

12.10 

17.4 

17.30       i 

17.4 
17.3 

C 

29.7 

17.33 

29.9 

C 

2!«.8 

30.0 

29.87 

29.8 
29.9 

29.83 

Blank  to  h,'f//,d  In  hi,  ,st,uh,>(. 


Method  «. 


Mean  value 
for/. 


I-en.s. 


Method  ft. 
/■ 


Mean  value 
for/. 


J*^S^^' 


■^^m^^r^'-s^mij^. 


UOIIT. 


63 


1 


ax.  TO  FIND  THE  FiKAL  LENGTH  OF  A  CONVEX  LENS 
BY  THE  DISTANCES  OF  THE  OBJECT  AND  IMAGE 
FROM  THE  LENS.     METHOD  II. 

References — As  in  Method  I. 

Apparatus  Required — In  addition  to  that  of  Method  I,  a 
lamp  and  tine  wire  grating  or  other  suitable  object  for  illinni- 
nation  will  be  requireil. 

Theory  of  Experiment.— As  before,  n  and  v  being  the  re- 
spective distances  of  the  object  and  image  from  the  lens, 
we  have 

from  which/  may  be  readilv  calculated,  if  v  and  v  be  observed. 

Practical  Directions — Mount  on  one  of  tlio  stands  the  fine 
wire  grating,  with  the  plane  at  right  angles  to  the  bi-nch. 
Cover  the  grating  with  a  large  sheet  of  paper  having  u 
small  holp  near  the  centre. 

Mount  the  lens  on  the  second  or  middle  stand,  so  that  its 
axis  lies  along  the  bench  in  a  horizontal  line  with  the  centre 
of  the  hole. 

The  thinl  stand  carries  the  ground-ghiss  screen,  mounted 
at  right  angles  to  the  bench,  so  as  to  receive  the  image  of  the 
wire  gauze. 

The  object,  lens,  and  ground-glass  screen  should  occnpv 
he  same  positions  in  relation  to  the  indexes  carried  bv  them. 

Place  the  light  directly  behin  1  the  hole  in  the  pajwir,  and 
us  close  to  it  as  possible. 

Adjust  the  positii.ns  of  the  lens  and  screen  along  the  bench 
until  a  clearly  detined  image  of  the  illuminated  object  is 
obtained 

If  the  focal  length  of  the  lens  be  less  than  one-fourth  the 
available  length  ..f  the  bench,  an  image  of  the  illuminatctl 
wire  grating  can  in  tills  ni.uiniT  be  readily  obtained. 


.-^  ^^  r'H^f^^:'^' 


M 


LABOHATOHY  PUYSICS 


The  image  is  best  observed  from  behind  the  ground-glass 
Read  the  position  of  the  indexes  carried  by  the  wir«  screen 
lens,  and  ground-glass  screen.  ' 

Tlie  adjustment  of  the  jwsition  of  tlie  lens  should  be  nuide 
three  tunes,  and  a  mean  ot  the  readings  taken  for  a  and  v. 

Calculate  from  //  and  v,  the  distances  of  the  ohjt«t  ui, 
image  from  the  lens,  the  value  of/,  using  formula  (1). 

liepeat  the  observations  three  times,  and  take  the  mean 
value  of/". 

If  there  be  too  nmeh  glare  from  the  light  behind  the  wire 
grating,  it  will  be  well  to  cover  it  with  thin  white  paper. 
Thecxperiuient  nmst  be  performed  in  a  darkened  room. 
Example — Enter  results  thus : 
Lens  A. 


It. 

Mean  u. 

V. 

Meant;. 

'    /. 

Mean  /. 

30.     ) 
29.8  ^ 
30.1  ) 

I 

29.96 

20.    ) 
20.2;- 
19.9^ 

20.08 

1          ^^ 

40. 

17. n 

j 

/'         40.2 
40.4 

40.3 

1         16.9[ 
'         16.7 

16.9 

11.9 

36.    ) 
35.8- 
36. a) 

36.0 
Blank  t 

IS. 3  ) 

i         18.4  \ 

18.0) 

18.2 

1-M 

13 

0  heJiUed  h 

<  hij  Hudet 

it. 

u. 

Mean  u. 

V. 

Mf.  ri  i>. 

1 

1        /• 

Mean/. 

. 

.  1 

UUllT. 


22.  TO  FIND  THE  FOCAL  LENGTH  OF  A  CONVEX  LENS 
BY    CHANGING    THE    POSITION   OF    THE    LENS 
METHOD  lU 

References.— Same  as  M.tlio*!  \{a). 

Apparatus  Required      As  in  ]\I  thud  II. 

Theory  of  Experiment— If  tlic  distaticp  })etween  ol.jcct 
and  wrt-en  l>c  more  than  four  time.-<  tlie  focal  length  of  th.* 
lens,  tlie  lens  will  have  two  positions  wliere  a  rleaily  defined 
image  of  the  olgect  will  be  o!  *ained  on  tlie  groiind-glafs,  screen. 

Let  tlte  dihtjince  between  the  object  and  screen  be  /,  that 
between  the  two  j-ositions  of  the  lens  a,  and.  as  before, /the 
focal  length.     Then  we  have 

111         1     ^       ,      . 

-^  -r  ~  =  -T.,  for  the  hrst  position. 


and 


— h  -  =  "/.»  for  the  second 
^'.       «'.       / 


Fnrther,  it  is  clear,  since  I  is  constant,  that  v  —  r  and 
V  =  n, ;  that  is,  the  lens  will  be  at  the  same  distance  from 
the  ground-gla:ss  screen  in  the  second  case  as  it  was  fiom  the 
ol»ject  in  the  first. 

Hence  we  have 


u  -\-  V  =  I,      I/,  —  It  z=  a,     ?/,  =  i<, 


and  tlierefore 


/  -  a 


u  = 


/  +" 


o       ' 


Substituting  these  values  of   >i  and  o  in  equation  (1),  we 
obtain 

f  =       ^. ■i\ 


66 


LA nouA  roH  r  nirsics. 


TIio  above  rulatiofi  in  iiide|)Cii(!ent  of  the  (ligtAtict's  l)ctween 
the  tiurfuce  of  the  lunn  and  tho  ol»ject  and  image,  which  dis- 
tances are  uuich  /nore  ditticnlt  to  nieasure  accnrately  than  tho 
distance  a. 

For  accurate  work  it  must,  however,  be  remembered  that 
n  -{-  t)  in  not  e<iual  to  /,  a^  the  <li«tai.  es  u  and  v  are  not 
strictly  measured  from  one  point,  but  from  the  principal 
points  of  the  lens.  These  princi|)al  points  are  one*Jiird  the 
thickness  of  tho  lens  apart,  and  therefore  the  formula  for 
thick  lenses  or  combinations  would  have  to  be  corrected.  This 
correction,  however,  for  an  ordinary  long-focus  lens  of  20  cm. 
or  so,  is  unimportant. 

Practical  Directions.— The  wljustments  are  as  in  Method 
II.  Bring  the  lens  up  to  the  gnmnd-glass  screen  until  a 
sharp  image  of  the  object  is  obtained.  If  this  image  is  in- 
conveniently snuili,  the  ground-glass  screen  should  be  moved 
nearer  the  object,  and  the  lens  refocussed. 

Read  the  index  carried  by  the  lens. 

Move  the  lens  into  the  other  jwsition  near  the  object,  the 
ground-glass  screen  remaining  fixed,  until  a  sharp  image  of  the 
object  is  again  obtained  in  the  ground  glass. 

Read  the  lens  index  iigain. 

The  diflferonce  between  the  two  readings  gives  a. 

Read  the  indexes  canied  by  the  object  and  ground-glass 
screen.     Hence  the  distance  I. 

The  observations  for  a  should  be  made  by  adjusting  the 
lens  three  times  in  each  position,  and  a  mean  taken. 

A  more  accurate  way  of  determining  the  coincidence  of 
the  image  with  the  ground-glass  screen  is  to  substitute  for  it 
a  wire  gauze  with  its  wires  inclined  at  an  angle  of  45°  to  the 
wires  of  the  gauze  used  for  die  object. 

Focus  a  small  reading-telescope  of  high  power  on  the 
wires  of  the  second  screen. 


.t;->gl.^jir:^^^v:'^r.-.-^i./^-^^ 


--•••'■y 


rf^y.: 


LidJir. 


07 


Move  tlu;  Ilmi!*  until,  on  looking  tlmmgli  tli»j  tele8co|H',  the 
wirurt  of  the  ilhiii'  Muted  hereen  arc  w;cii  iu  focun  with  the 
other.  No  cuiilijHiun  ut'  ocreeii  iiiul  iiiiuge  can  urise  if  the  two 
bo  inclined  to  eiwh  other  jw  suggebted. 

It  irt  iniportitiit  tluit  the  image  bcreen  should  not  he  u»  >  ';d 
after  i"oeUi»f*ing  the  telewjope. 

A  good  pliiii  i^  to  Uhe  u  imwerful  nil.}  ■  ,' -i  liive  the  posi- 
tive ejopiece  of  a  teleHco|K.',  iintl  moi  i  i  ii  -< .  nd 
8creen-otan«l  bo  !i8  to  ni(»ve  with  it.  ^!  ■  |  ■  m  ■•  ii  .d  ..  ;e 
can  be  obtiiined  in  thin  way. 

Example. — Kntur  remdtb  thub: 


100 


72.1 
72.0 


Me^      ,1 


:2.lo 


12.0 


Jiliink  til  hf  fUtd  hi  hij  fi(>ulent. 


Mean  ii 


"a^aa^ESlBeeJU^^Xr^fM.^irt  ^J!S 


Ill 


68 


LABORATORY  PUT81C8. 


23.  TO  FIND  THE  FOCAL  LENGTH  OF  A  CONVEX  LENS 
FROM  THE  SIZE  OF  THE  MAGNIFIED  IMAGES. 
METHOD  IV. 

References. — As  in  Metliod  II. 

Apparatus  Required. — A  transparent  scale,  finely  cliviikd 
(an  ordinary  opal-glass  scale  answers  well);  a  large  wliite- 
pajier  screen ;  a  lens  of  rather  «liort  focns;  a  pair  of  dividers; 
a  lamp  and  optical  bencli. 

Theory  of  Experiment. — Let  /  be  the  length  of  a  division 
of  the  tmnsparent  scale  which  is  nsed  as  an  object.  lA't  L  be 
the  length  of  a  division  of  the  magnified  image.  Let  v  ho 
the  distance  of  the  screen  from  the  centre  of  the  lens  when  a 
sharp  ima^c  occurs  on  it. 

Then  we  have  the  ordinary  relation 


L  +  l  =  i 


0) 


where  n  is  the  distance  from  the  illnminated  scale  to  the  lens. 
We  also  have  the  relation 

LI  \        L 


or 


Iv' 


Hence  by  substituting  in  (1)  we  obtain 

/ 


f  = 


(2) 


/-  +  / 

which  is  the  relation  required. 

Practical  Directions. — As  in  j)revious  methods,  the  axis  of 
the  lens  must  lie  along  the  bench  and  in  the  same  horizont.al 
as  tlie  centre  oi  the  illuminated  scale. 


•This  mftliod  is  applicaWe  t«  Miii-k  l»'iist'>  or  comhina'ions  when  tbe 
distance  Ix^tween  tbe  priiirii-al  points  cannot  1)P  nojripcted. 


5E^32t£^ 


^W^: 

-^:' 


1.10  UT. 


69 


i 


See  that  the  iiKle.\  carried  \\y  the  lens  is  in  the  same  plane 
H8  the  centre  oi  the  lcni>,  and  that  the  index  of  the  screen  lies 
in  the  plane  of  tlie  screen. 

Place  the  lens  at  a  little  greater  distance  than  its  focal 
length  from  the  scale. 

Move  up  the  white  screen  until  a  sharply  defined  image 
of  the  scale  division  is  obtained. 

Measure  to  ^^  mm.  the  length  of  as  great  a  number  of 
inagiiitied  divisions  m  are  obtained  on  the  screen. 

Itead  the  distance  between  the  lens  and  surface  of  the 
screen. 

(^alculate  the  value  of  a  sinirle  uiaj'nitied  division  in  ternl^ 
of  the  ol)je('t  .*<cule. 

Uepe^it  the  observations  three  times,  and  take  the  mean 
value  of/' calculated  from  formula  {'!). 

Example Enter  results  thus: 


V 

/ 

L 

/ 

8.j  0 
63.5 

48  7 

1 
1 

1 

3.15 
2.12 
1.4 

20.40 
20.30 
20.30 

Mean  value  uf 

•• 

20.33 

Bf(nik  io  hi'  Jill  til  in  hij  .sfudcnt. 


V 

1 

/. 

/ 

Mean  value  ot 

f 

•' 

ro 


LABOR ATOliY  PHYSICS. 


24.  TO  DETERMINE  THE  FOCAL  LENGTH  OF  A  CON- 
CAVE LENS  BY  THE  DIVERGENCE  OF  THE  R^i- 
FRACTED  RAYS.     METHOD  I. 


References — Watson,  p.  4S1 ;  Knott,  pt.  11.  p.  '_'«>»; 
Hastings  and  Beach,  p.  619;  Kicliols  and  Kranklin,  j).  4."i; 
Ames,  p.  440;  Antliony  and  Brackott,  p.  41 -J. 

Apparatus  Required. — An  t'lenientarv  optical  IkmicIi;  a 
moderately  long  focns  concave  lens;  a  lamp;  a  gronnd-glass 
soreen;  a  black-paper  screen  witli  two  sjiiall  apertures  not 
greater  than  the  width  of  the  lens  aj)art;  a  pair  of  dividers; 
a  centimeter  scale. 

Theory  of  Experiment.— -Let  h  and  r  he  the  respective  dis- 
tances of  the  source  of  light  and  the  virtual  image  from  the 
face  of  the  concave  lens  A  II. 

Then  we  have  the  ordinary  formula  for /*,  the  focal  Icno'th 
of  concave  lenses, 


1 

7 


1 

I' 


1 


0) 


% 


V  and  r  being  in  this  case  iM.th  on  the  same  >idi-  of  the  iens. 
Of  tlu'se  values  u  can  l)e  measured  dircctlv. 


Fi.i.    17. 


If    imw  the   face  i.t'  \. 


\y   Ifiis    III 


black    paper   with    two   ;!]Hi't!i!i 


(•  coviTcd  witli    ;i   sJuM't   of 
''.    "",,    till-    liiiht    ji,t>-iii<.v 


I.WIIT. 


throtigli  these  H|)erture8  will  give  two  bright  patches  of  lig'lit, 
6,  i„  on  a  acreen  placed  to  receive  them.     Then 


V 


V  -\-  ccj 


aa. 


cc. 


or 


V  ■=■ 


bb.  —  (ui. 


Since  a  a^^  b  A„  c  i\  can  be  measured,  v  can  be  calcu- 
lated. 

Substituting  in  formula  (1), /'can  be  calfulated. 

Practical  Directions Motuit  tiie  lens  in  the  n)iddle  stan<i 

with  its  axis  horizuntal  and  along  the  l)eneh. 

Make  two  tine  holes  in  the  black  paj)er  not  more  than  2 
or  3  cm.  apart,  and  iix  it  to  the  surface  of  the  lens  so  that  the 
apertures  are  central  with  regard  to  it. 

Mount  the  lamp  (an  incandescent  lamp,  with  the  lilament 
edge  on,  answers  well)  on  one  of  tlie  outside  stands. 

Adjust  the  height  of  the  lamp  so  that  the  centre  of  the 
Hlament  is  in  the  same  horizontal  as  the  axis  of  the  lens. 

Mount  the  ground-glass  screen  behind  the  lens  at  right 
angles  to  the  l>ench,  so  as  to  receive  the  divergent  rays  of  light. 
Move  the  lens  along  the  bench  until  a  considerable  divergence 
i.;  obtained. 

Measure  carefully  by  means  of  the  dividers  and  scale  the 
<listance  between  the  centres  of  the  bright  spots  on  the  ground- 
glass  screen,  and  also  to  the  tenth  of  a  millimeter  the  distance 
between  the  aj)ertures. 

Read  on  the  bench  the  distances  of  the  lamp  and  ground- 
glass  screen  from  the  surface  ctf  the  lens  next  the  apertures. 
The  ri'lative.  ]>ositioii8  of  tlif  lump,  lens,  antl  ground-gluss 
K'reen  to  their  indexes  should  be  carefully  ullitwed  for.  The 
adjustment  of  the  position  ot   the  lens  should  be  made  three 


7l*  LA  noli  AWRY  PHYSICS. 

timi's,   hikI    the   mean    of    the  oalcuhited    vuhie   of    ,'   taken. 
Calcuhite  r  from  formula  (2),  ami  Milmtitute  in  (1)  for  f. 
Example — Enter  results  thus : 


77.0 


hi,. 


2  0 

03 

«j 

6.4 

2.0 

6.3 

26.r) 

26.5 
26.5 


12.33 
12.33 
12.32 


14.6 


Ulonk  to  hcjilhil  In  hi/  ,sfi((/t/if. 


u. 

.1-.,. 

hht. 

(■<■,. 

i: 

/■ 

25.  TO  DETERMINE  THE  FOCAL  LENGTH  OF  A  CON- 
CAVE LENS  BY  AN  AUXILLARY  CONVEX  LENS. 
METHOD  U. 

References. — As  in  previon.*  vxjx'nmejit. 

Apparatus  Required.— The  snuw  as  in  Method  I,  except  tl)e 
black- paper  screen,  and,  in  a<l(lition,  a  .>;nital)le  convex  lens  of 
known  focal  leiiirth. 

Theory  of  Experiment — A  more  accurate  method  than  tlie 
precedini;  is  ohtained  !•>•  niakin<,r  a  comhination  witli  a  convex 
lens  of  sufficient  power  to  r.iider  the  comhination  slij;htly 
convex.  Suppose  A /i  {V\<r.  Is)  a  concave  len.s,  and  CD  & 
convex  lens  of  known  focal  len<rth,  so  that  the  two  together 
make  a  convex  sv.'^ttm. 


I 


LIGHT. 


r8 


CoiisiilcT  tlieliiflit  traversing  tlic  ('((iK'avc  leny  from  a  !>ri"!ir 
ol»ject  at  (f.  It  is  refracted  so  as  to  form  a  virtual  imaiie  at 
a,  and  we  have  therefore 


1^ 

V 


1 

a 


1 


0) 


wliere  aM=  r,  and  (9J/=  ?/,  and/' is  the  focal  length  of  the 
concave  lens. 


Fiii.   18. 

The  rays  are  again  lent  from  the  path  aC,  and  refracted 
to  a  focus  i)oiiit  b  l>y  the  convex  lens. 

Then  as  far  as  the  convex  lens  is  concerned  the  source  of 
light  is  at  a. 

We  have,  therefore, 


1+1  =  -'. 


V 


(2) 


where  </3/=  v,  and  Mb  =  r„  and/',  is  the  focal  length  of  the 
convex  lens. 

Let  /'be  the  ft)cal  length  of  the  conihination. 

Then  the  light  from  (>  is  brought  to  a  focus  at  b  by  the 
combination  of  the  two  lotises. 

It  follcws,  therefore,  that 


u   ^  (\         F 


(-0 


74 


LA  BO  HA  TOR  T  I'll  VSirS. 


Ilenee,  coinhiiiinj;  (1),  (2),  and  (3),  we  obtain  the  relation 
J.  -  i.  _   1 


or 


(4) 


/^can  be  calculated  from  formula  (8),  andy*  from  formula  (4), 
/',  being  known  or  found  separately. 

Practical  Directions. — The  adjustments  and  observations 
are  the  same  both  for  the  convex  lens  and  the  combination,  as 
i'l  the  case  of  convex  lenses. 

It  is  readily  seen  In*  inspection  of  formula  (4)  that  some 
ire  is  necessary  in  choosing  the  auxiliary  lens.    For  \i  F  —  f^ 
>e  small,  small  err  's  in  meJisuring  them,  unless  the   errors 
■  same  direction,  would  result  in  a  large 
'tivex    lens  should    therefore  be   chosen 
iiference  /'—/',  a.s  large  as  possible,  or 
mid  be  ecjuivalent   to  a  lens  with  very 
hat /'is  very  nearly  eipial  to/',, 
result    thus: 


liappen  to  be  in  ' 
error   iii  /'.      Th< 
so  as  to  mak 
the    combinat 
slight  coTivexi'    , 


Example.     Ki 


vex 

lis. 

•  ibservations  for  F. 

F. 

/ 

n. 

'"!■ 

12 

11    ;( 
12.1 

120 
120.5 
119. S 

165.9 
165.4 
IWl.l 

<i9.6 
69.7 
•19.6 

14  5 
14  5 
14.5 

Jilank  to  h>\p'll>'(l  hi  hy  xtiKhitt. 


Coin-ex 

I.<M1<(. 


OhxfrvaMoim  for  F. 


F. 


LKlllT. 


75 


26.   (i^  TO  CONSTRUCT  A  MISCROSCOPE. 
(2)  TO  CONSTRUCT  A  TELESCOPE. 

References. — Anthony  ami  Hrackett.  \>.  42."»;  Ames,  i)p. 
450-4r»2;  Ilastinps  and  Ikwli,  \>\^.  ♦»31-r»37;  Jiaiker,  pp. 
456-471;  Knott,  pt.  11.  p.  2s4;  Nifliols  and  Franklin, 
vol.  HI.  pp  ■)7-7l :  Watson,  p]).  4.nJ»-41»3. 

Apparatus  Required — Three  short-fdcns  lenses  and  one 
long-focus  lens,  snitaitly  mounted;  a  centimeter  sitale;  a  ]iiece 
of  wire  gauze  \\\  a  damp-stand. 

Theory  of  Experiment. — (I)  The  Misor<n«^i>})e. — If  an 
object  All  he  placed  in  front  of  a  short-focus  lens  PQ  so  as 
to  he  just  heyond  its  principal  focus,  a  real  inverted  and 
slightly  magidticd  image  of  the  ohject  will  he  formed  on  the 
opposite  side  of  the  lens  tVom  .1  II  as  AJi^. 

If  now  a  second  lens,  J/.\'.  I>e  placed  so  that  the  image 
AJi^  is  just  inside  its  princi|ial  focus,  a  vertical  and  magid- 
fied  image  of  AJi^  will  he  produced  on  the  same  side  (tf  MN 
as  A.li,^  see  A „/>,,,  I' ig .  1 J » . 


Fio.  19. 


The  lens  MX  with  re.-pcct  to  the  image  /I,//,  forms  a 
siu)ple  mis<M-t)sc<*|K'.  The  two  lenses  with  re-|»ect  to  the 
((hject  .1  A'  form  a  conipouml  miscroscopc. 

/V,>  i>  Ciillcil  the  ohjcct-glass,   .)/.\'  tlie  eyepiece. 


ilB 


78 


LA  BOrtA  TOR  V  PII YSICS. 


(2)  Tlte  TeleHoope. — The  telu»cojie  is  cuii«tructed  on  the 
saiue  principal  an  the  nii8croHco])c.  In  the  case  uf  the  tele- 
scope, however,  the  object-glass  is  a  h>ng-focu8  lens  and  forms 
a  diminished  image  of  a  dUtant  object  instead  of  a  magnified 
image  of  a  near  object.  As  in  the  case  of  the  miscroscope, 
the  eyepiece  \s  used  to  magnify  the  image  obtained  by  means 
of  the  object-glass. 

Practical  Directions.— (1)  Tlte  Mincroscope. — A  centi- 
meter scale,  held  vertically,  makes  a  suitable  object. 

In  front  of  it  place  one  of  the  short-focus  lenses  at  a  dis- 
tance a  little  greater  than  its  focal  length.  A  suitable  ])06i- 
tioii  can  be  found  by  placing  the  lens  quite  near  the  object 
and  then  moving  it  gradually  away  until  a  real  inverted 
image  is  seen  between  the  eye  and  the  lens. 

To  find  the  exact  position  of  the  image  so  that  the  eye- 
piece can  be  adjusted,  a  piece  of  wire  gauze,  mounted  on  a 
stand,  can  be  used.  Adjust  the  position  of  the  gauze  until  it 
appears  to  coincide  ',\ith  the  image. 

The  point  of  exact  coincidence  can  be  obtained  bv  mov- 
ing the  eye  Inick  and  forth  in  a  plane  parallel  to  the  gauze 
and  atijusting  until  the  gauze  and  image  continue  to  occupy 
the  same  relative  position  from  whatever  point  they  be 
viewed. 

Take  another  of  the  short  focus  lenses  and  focus  it  upon 
the  vkV^v  of  the  gauze  coincident  with  the  image. 

licuiove  the  gauze,  and  a  magniticd  image  of  the  scale 
will  be  seen. 

Mejisiire  <i  and  h,  the  distances  from  the  object  to  the 
objeetglass  and  from  the  object-glass  to  the  eye])iece 
resiH-ctively. 

Kej>eat  the  observations  three  times,  changing  the  dis- 
tance (/  in  each  case. 

{'!)  The  a^ljll^tments  for  the  telescope   a-e   exactly   the 


LIOUT. 


77 


same  aa  for  tlie  luiscroscopc,  tlio  otily  difference  lieiiig  tliat 
the  ohject-f^lass  is  a  long-focus  iens  and  its  distaiico  fruin  tlio 
)hjeet  much  greater. 

Example.— Enter  results  thus: 


TeleHCope. 


74.5 
168.1 
121.  (J 


lilduk  to  he  JiUed  in  hy  tttudent. 


Hiscroscope. 

Teleucope. 

a 

b 

a                                   b 

• 

27.   TO  DETERMINE  THE  MAGNIFYING  POWER  OF   A 

MICROSCOPE. 

References. — As  in  Experiment  26. 

Apparatus  Required. — A  compound  microscope;  two  mil- 
limeter scales. 

Theory  of  Experiment. — The  magnifying  power  of  a 
micro.*icoi>e  is  the  ratio  of  tlie  angle  subtended  at  the  eye  by 
tlie  image  tu  that  subtended  by  the  object,  both  l)eing  at  the 
<li.*tance  of  distinct  vision.  al)out  2.">  cm.  If,  therefore,  a 
microscope  bo  focusse<l  on  a  finely  divided  scale  and  the 
image  be  observed  with  one  eye,  while  the  other  eye  looks  at 


I 


r«^*' 


78 


LA  no  11 A  roil  y  rii  raws. 


P^M^i 


a  hc'coinl  similarly  divided  sc-ak'.  2.'.  ciii.  distant  and  so  placed 
that  the  iiiia^'f  of  the  tirht  apjK'iiirt  to  coincide  with  it,  the 
iHiiidier  of  ilivisioiis  of  the  Hccmid  scale  covered  l»v  one  of  the 
inagnitied  ilivisioiis  of  tlje  imaj^e  gives  the  inagnifv  iiig  iH>wer. 
Siiiiihirly  if  the  iiiiignifyiug  powers  of  e.ch  of  the  lenses 
he  ohserved,  their  product  will  he  the  magnifying  jjower  of 
the  inieroscojR'. 

Practical  Directions. — (i)  Focus  the  microscope  upon  u 
millimeter  scale. 

Place  another  millimeter  scale  at  the  side  of  the  instru- 
ment at  a  distiince  of  ahout  25  cm. 

Looking  thnuigh  the  microscope  with  one  eye,  adjust  the 
l)osition  of  the  .-econd  scale  until  the  inuige  of  the  first  as 
seen  in  the  microscope  api»ears  to  coincide  with  the  second 
wale  as  seen  hy  the  other  eye  al(»ng  the  side  of  tlu-  micro- 
seope.  Count  the  immher  of  scale  divisions  of  the  second 
scale  covered  hy  as  many  of  the  niagnitietl  divisions  of  the 
image  as  can  he  accurately  ohserved. 

Denoting  the  niimher  of  divisions  of  scale  hy  (t,  the  cor- 
responding divisions  of  the  image  hy  b,  and  the  mugnifving 
[>ower  hy  J/,  then 


M 


a 
h 


(1) 


Repeat  the  ohservations  several  times  and  take  a  mean  of 
the  results. 

(•J)  The  magnifying  powers  of  tlie  eyepiece  and  the 
ohject-glass  may  he  found  separately  hy  a  similar  method,  if 
the  microscope  contain  in  the  eyepiece  a  micrometer  scale 
the  vahh'  of  the  divisions  of  which  are  known. 

Focu>  the  microM'ope  on  the  millimeter  scale  and  note  the 
numl)er  of  division>  of  the  image,  which  !>  magiiitied  hv  hoth 
the  eye[>iete  and  the  olijeet-glass,  covered  hy  a  numher  of 
divisitius  of  the  nucromcter  f-eale,  whic!.  is  magnitied  \)y  the 
evepiicc  oiilv. 


;:?3Ki&i^saF 


■f^i.'-kiODM&X: 


uuur. 


70 


Tlio  ratio  of  the  two,  expressed  in  the  same  units,  gives 
the  magnifying  power  of  the  ol)ject-gIaiw. 

Thus,  if  we  denote  the  magnifying  {K)wer  of  tlie  ohject- 
glass  by  ;«,  tlie  divisions  of  the  scale  by  A. ,  the  eorreK|)ond- 
ing  micrometer  divisions  by  c,  and  tlie  constant,  re<piired  to 
reduce  micrometer  divisions  to  scale  divisions  by  rf,  then 


m 


c6 


(-' 


Observe  now,  with  one  eye  along  the  side  of  the  micn.- 
BcoiK',  the  number  of  divisions  of  the  scale  covered  l>v  a 
iletinito  number  of  divisii>ns  of  the  micrometer  scale  as  seen 
by  tlie  other  eye  through  the  nucroscope. 

Since  tlie  micn»meter  scale  is  imigiiitied  by  the  eyepiece 
o\\\y,  the  ratio  of  these  two,  when  expressed  in  the  same 
units,  gives  the  magnifying  power  of  the  eyepiece. 

If  b,  l>e  the  sade  divisions,  t\  the  corresponding  nucroni- 
eter  divisions,  and  m^  the  magnifying  power  of  the  eyej)iece, 
then 

h. 

(3) 


'e.6 


The  product,  ///  .  /«,,  gives  ^f. 

Iie[K.'at  the  observations  several  times  for  both  eve]iicct' 
an<l  objcct-gliiss. 

Example. — Enter  results  thus: 

FlKKT    MlTlloU. 


42 
4'J 


ai 

21 
21 


"Shixu  viilur  nf  M. 


i^imj 


IE 


MICROCOPY   RBOIUTION   TEST  CHART 

(ANSI  and  ISO  TEST  CHART  No.  2) 


1.0 


1.1 


50     ^^^ 

"      3.2 


|» 


KUI* 


1^ 
1 40 


|2.5 
2.2 


1^ 

1.8 
1.6 


^  /1PPLIED  IIVMGE    Inc 

^^-  1653  East  Main  Street 

Ks  Rochester,   Ne«   York         14609       USA 

.as  (716)    482  -  0300  -  Phone 

^5  (716)   288  -  5989  -  Fox 


•'<k!£:^. 


<  i 


80 


LABORATORY  PIITSICS. 
Second  Method. 


i 

Ohject-fclass. 

Eyepiece. 

m, 

2.88 

2.88 
2.88 

ii 

''1 

c 

m 

6, 

11 

6 

11 

.63 

3 
o 

34 
23 
34 

7.14 
7.24 

7.14 

20 
10 
20 

20.57 
20.80 
20.57 

20.64 

Mean 

value  of  M 

r 

.. 

BhinJca  to  he ^P led  in  by  student . 
FiusT  Method. 


.V 


Mean  value  of  M. 


Second  Mkthod. 


Object-glass. 


EyepiVce. 


6, 


m        j        h,        !        c, 


I 


it 


Muaii  v!,hie  of  M. 


w^i^f^^am 


M^^^-i^Sf¥f^.^sm^»i^k<i^^^^i^m^m^ms^fm: 


LIOiIT. 


81 


28.  TO  DETERMINE    THE   MAGNIFYING  POWER  OF  A 

TELESCOPE. 

References. —As  in  Experiment  26. 

Apparatus  Required.— A  white  paper  scale  abont  60  cm. 
long;  two  strips  of  white  paper;  a  telescope;  u  tape 
mejisure. 

Theory  of  Experiment.  -  The  mu-nifyin-  power  of  a 
telescope  is  the  ratio  of  the  angle  subten<led  at  the  eve  by  the 
image  in  the  telescope  to  the  angle  subtended  I)y  the  object, 
the  telesco])e  being  so  focussed  that  the  object  and  imac^e  are 
at  the  same  distance  from  the  eye.  The  angles  subtended  at 
the  eye  by  the  object  and  image  being  very  small,  this  ratio 
will  be  the  same  as  the  ratio  of  the  magnitudes  of  the  image 
and  object,  their  positions  being  as  stated  above. 

Hence,  if  a  telescope  be  focussed  on  a  graduated  scale  or 
other  distant  object  and  so  adjusted  that  the  object  and  imajre 
are  at  the  same  distance,  D,  from  the  eye,  the  magnifying 
power  of  the  telescope  for  the  distance  D  is  given''  by  the 
equation 

a  ' 

where  a  is  the  number  of  image  divisions  coverings,  division^ 
of  the  scale. 

Practical  Directions.-Fasten  upon  the  wall  of  the  labora- 
tory in  a  vertical  posi;  ion  the  centimeter  scale.  At  equal  dis- 
tances from  the  ends  of  the  scale,  and  at  right  angles  to  it 
fasten  the  two  strips  of  i)aper,  the  muldle  of  the  paper  bein-'r 
m  the  axis  of  the  scale  in  each  cuse.  The  distance  between 
the  strips  of  paper  should  be  about  75  cm. 

Taking  the  telescope  3  or  4  meters  away,  focus  it  upon  the 
scale. 


ftTi¥m»'"^*f'^m*^^^I^'W»^y 


^^?S^>:%2E^^')«ft 


-»*sJ5rs»> 


Ti;^¥&mm 


82 


LABOBATORT  PHYSICS. 


Looking  through  the  telescope  with  one  eye  and  observing 
tlie  unmagnified  scale  with  the  other,  the  image  will  appear 
projected  against  the  scale. 

Adjust  the  position  of  the  eyepiece  until  the  image 
occupies  the  same  position  as  the  scale.  If  the  eyepiece  has 
been  focussed  on  the  cross-hairs,  it  will  be  necessary  to  pull  it 
out  slightly. 

The  exact  position  of  coincidence  of  image  and  scale  can 
be  determined  as  in  previous  experiments  by  adjusting  the  eye- 
l)iece  until  the  scale  and  image  continue  to  occupy  the  same 
"elative  position  when  the  eyes  are  moved  back  and  forth 
across  the  field. 

Having  found  the  position  of  coincidence,  read  the  number 
of  image  divisions,  a,  covered  by  the  distance  between  the 
two  strips  of  white  paper. 

Repeat  the  observations  several  times. 

Measure  the  distance  «,  between  the  strips  of  pajier. 

Measure  the  distance  D. 

Calculate  M. 

Repeat  the  observation  three  times  for  different  distances 
of  telescope  and  object. 

Example. — Enter  results  thus: 


h 


l>  (meters). 

". 

Readinfcs  for  o. 

Mean  a. 

M 

4.35 

75 

5.1 
5.0 
4.8 

4.97 

15.1 

5.75 

75 

5.2 
5.2 
5.8 

5.28 

14.3 

7.28 

75 

5.7 
5.7 

5.8 

5.73 

12.5 

■  :!•  'tmjs^s^^s^isip^^^^'^^^^m-s^ 


i 


LIGHT. 
Blank  to  he  filled  In  hy  student. 

•'eailiUKs  for  a.  Mean  a. 


83 


M 


29.  THE  SPECTROSCOPE. 

(1)  TO  MAP  THE  SOLAR  SI-ECTRUM  AND  PLOT  THE 
CALIBRATION  CURVE  OF  THE  INSTRUMENT 

(2)  TO  MAP  A  BRIGHT-LINE  SPECTRUM  AND  MAKE 
A  TABLE  OF  CORRESPONDING  WAVE-LENGTHS. 

References.— Nichols  and  FraiikliTi,  vol.  iii.  p.  TtJ;  Car- 
liart,  pt.  I.  p.  293;  Anthony  and  lirackett,  ]>]).  439-44-I-; 
Ames,  pp.  455-467;  Barker,  pp.  449-462;  Hastings  and 
IJeat'h,  pp.  704-710;  Watson,  pp.  £14-518;  Knott,  pt.  11. 
pp.  ;}24-32s. 

Apparatus  Required.— A  spectroscope  with  niicronieter 
•scale;  I'liicker  tubes  containing  II,  O,  CO,  N,  etc. ;  a  small 
induction-coil;  a  two- volt  storage-battery;  a  map  of  the  solar 
8j)e('trutn;  a  clamp-staud  for  PHicker  tubes;  a  striding  spirit- 
level;  some  small  connecting  wires. 

Theory  of  Experiment.— For  tlie  theory  of  the  experiment 
read  carefully  the  chapters  on  dispersion  and  the  solar  spec- 
truiit  in  any  of  the  above  references. 


^JR?^^:i«^^i?^i'j: 


W^'^^i^k 


8:1 


LABOHAWliY  PHYSICS. 


Practical  HhtcMons.—AdJuMtment  of  tlm  Indrument. — 
Focus  tlie  telescope  by  the  metliod  of  parallax  on  a  distant 
object.  To  do  this  it  will  generally  be  necessary  to  unscrew 
it  from  the  instrument. 

Replace  the  telescope,  and,  the  prism  having  been  re- 
moved, view  the  slit  direct  and  focus  the  colliinator.  This 
may  be  done  by  adjusting  the  length  of  t\w  cullimator-tube 
till  a  sharp  image  of  the  slit  is  seen  in  the  telescope. 

Level  the  collimator  and  telescope  by  means  of  the  spirit- 
level  and  level  ling-screws  attached  to  them.  If  their  vertical 
height  be  the  same,  their  axes  may  be  assumed  to  be  in  tlie 
same  plane. 

The  prism  should  have  iis  refracting  edges  at  right  angles 
to  the  above  plane.  To  insure  this,  level  the  prism  table  by 
the  screws  provided.  Before  clamping  down  the  prism,  it 
should  be  set  for  minimum  deviation,  as  explained  under  the 
spectrometer.  (See  adjustment  for  mininnim  deviation.  Ex- 
periment 8(,».) 

The  instrument  should  be  turned  to  the  window,  and,  if 
available,  direct  suidight  allowed  to  enter  the  collimator. 

Adjust  the  width  of  the  slit  till  sharp  narrow  images  of 
the  dark  lines  are  seen. 

If  the  spectrum  be  traversed  by  dark  bars  at  right  angles 
to  the  solar  lines,  this  is  probably  due  to  dust  in  the  slit. 
This  may  be  removed  by  introducing  the  sharpened  end  of 
a  match  into  the  slit  and  passing  it  up  and  down  a  few  times. 

Illuminate  the  slit  in  the  small  tube  containing  the  scale, 
and  clamp  the  tube  in  a  position  such  that  the  whole  length 
of  the  spectrum  is  covered  by  the  scale. 

Adjust  the  length  of  the  scale-tube  till  a  well-defined 
image  of  the  scale  is  seen  in  the  telescope,  after  reflection 
from  the  near  face  of  the  prism. 

It  may  be  that  the  s]ie('troscope  is  ]irovided  with  a  grad- 


iVuW^ 


^,^^''^fWL  TS^S^^JI 


LIOHT. 


86 


I 


i 


uated  circle,  in  which  case  the  scale  readings  will  be  read  at 
the  index  carried  by  the  telescope. 

(1)  Mapping  the  Solar  Spectrum. —With  the  aid  of  the 
map  of  the  solar  spectrum  observe  the  position  on  the  scale 
of  all  the  principal  dark  lines  visible,  aiid  draw  to  scale,  on 
section  paper,  a  map  similar  to  the  one  below,  Fig.  20. 

If  direct  sunlight  has  not  been  used,  there  will  probably 
be  no  lines  visil)le  in  the  red  end  before  B,  and  none  in  the 
violet  beyond  G. 

^a  B  C      D     E      61     F     g    Q       h        H    K 


.) 


Fig.  20. 


Plotting  the  Calibration  Curve  of  the  /nsiritment.~The 
following  table  gives  the  wave-lengths  of  the  principal  dark 
lines  in  millionths  of  a  millimeter. 


Designation. 

Wave-Ifngth. 

A 

760 

B 

686 

C  (H) 

656 

1>  (Na) 

589 

E  (C  aud  Fe) 

527 

b    (Mg) 

518 

F  (H) 

486 

G  (Fe) 

431 

H(C&) 

397 

K  (Ca) 

393 

With  the  aid  of  the  al)ove  table  plot  the  calibration  curve 
of  the  instrument. 

The  scale  readings  may  be  jilotted  as  abscisete  to  the  scale 
of  one  scale  division  equal  to  one  centimeter;  and  the  wave- 
lengths from  the  table  as  ordinates  to  the  scale  of  fifty  equal 
to  two  centimetors. 


^S?;.V:^^'F 


t^''m:^i^^'w<^^s[^^^'''^:?m;^'m^^mi^ii^'^W4'%^'W 


86 


LA  DOHA  TOR  Y  PH  YSICS. 


The  ourvo  so  drawn  will  be  similar  to  Fijr.  '21. 
(2)    7\>  M,,tsKr,'  the  Witvt-lt't„ft/,.s  of  i/u   l!,-!<jht  Lh„s  hi 
the  Spectraii,  <>f  ,i  (mhx.~\\'\{\w\\\.  clijiiiiriji^r  the  iidjiistrnt'iit  of 

CALIBRATION  CURVE 


I  i 


i 


*°°6  8  10^  W  U 

SCALE  READINGS 
Fm.  21. 
the  instrument,  set  up  a  Pliicker  tube.     If  tlie  side-ou  type 
is  used,  have  tlie  capillary  section  vertical  and  close  to  the  slit. 
In  the  case  of  the  end-on  type  the  capillary  section  should 
have  its  axis  in  line  with  the  axis  of  the  collimator. 

Connect  the  electrodes  of  the  tube  to  the  secondarv  ter- 
minals of  the  induction-coil,  and  the  primary  of  the  induction- 
coil  through  a  switcli  to  the  current  supply. 

For  the  current  supply  a  portable  storage-cell  will  be 
found  convenient. 


1  I 


y-M^^m-r^i:'.^:'^^. 


WmW^jmfmm'm 


J.TGIJT. 


87 


t  i 


See  tliat  the  contact-ltreaker  works  contimioiislv  without 
sparking. 

On  looking  thionj^h  the  tek'^cope  tlie  brigljt  lines  <lue  to 
the  incandescent  gas  sliould  be  seen.  It  may  he  necessary  to 
widen  the  slit  a  little. 

IdentijicatUm  of  the  Briijht  Linen. — Read  the  positi«)n8 
on  the  scale  of  the  bright  lines,  designating  them  by  their 
color  and  brightness,  and  determine  their  corresponding 
wave-lengths  by  the  caliliration  curve. 

Precautions. — If  the  contact-breaker  sticks,  start  it  at 
once,  otherwise  the  coil  may  be  burnt. 

Handle  the  Pliicker  tubes  carefully.  Do  not  alter  any  of 
the  adjustments  between  observing  tlie  dark  and  bright  lines. 

Example.— Enter  results  thus: 

SOLAR  SPfX'TUUM. 


Designation 
of  Line. 

Scale  Reading. 

Wave-Iencth 
from  Table. 

B 

7.16 

686 

C 

7.57 

656 

D 

8.73 

589 

E 

10.30 

526 

b 

10.61 

518 

F 

11.70 

486 

G 

14.60 

430 

Blank  to  he  filled  in  hy  student. 


Desiftnation 
of  Line. 

Scale  Reading. 

Wave-length 
from  Table. 

?r!^,  - '«,-.3riv'F^iir«*s^™c?w'rsrs5S5SPMW!«Ear.«i»P3!^^ 


88 


Laboratory  phtsics. 


linyJa-hne  Spectrum  of  0^uj,jen  and  IJydr<Hfni.~hy 
means  of  a  tube  containing  oxygen  and  anotlior  containing 
lijUrogen,  ilhnninated  hy  tlie  discliargu  fn.nj  the  coil,  the 
following  bright  lines  may  be  obberved  : 


Color  of  Line. 

Scal«>  Keadinj 

Oxygan 

lied 

830 

»85 

Yellow 

890 

Greeu 

985 

10.50 

11.80 

Blue 

12.85 

Hydrogen 

Red(C) 

7.55 

Blue(F) 

11.70 

Violet  (G) 

i4.ao 

WavelfUKth 
from  Cur\'f . 


617 
607 
572 
562 
523 
488 
470 


659 

480 
430 


Blank  to  he  Jill e  J  h,  hj  student. 


Color  of  Line. 


Scale  Reading. 


Wave-Ienffth 
from  Curve. 


LJOHT. 


89 


30.  TO  DETERMINE  THE  ANGLE  OF  A  PRISM  AND  TO 
FIND  ITS  REFRACTIVE  INDEX  BY  MEANS  OF  THE 
SPECTROMETER. 

References— Watson,  p.  41)5;  Carliart,  pt.  i.  p.  i>(»3. 
Apparatus  Required — A  eiKjrtroineter  having  a  vernier 
provided  for  the  prism  table  as  well  as  for  the  telescope;  a 
prism;  a  bunsen  burner;  a  spoon  of  platinum  f;.il  for  contain- 
ing the  salt  for  sodium  Hume;  gas-tubing;  a  spirit-level. 

Theory  of  Experiment.— The  Theory  of  Experiment  is  the 
same  as  that  for  "  The  Measurement  of  the  Angle  of  a  Prism 
by  Pin  Method,"  p.  40,  and  ''To  Find  the  Index  of  Kefrac 
tion  of  a  Prism,"  p.  46. 

Practical  Directions.— The  general  adjustmenis  are  the 
same  iis  for  the  spectroscope,  p.  84. 

To  Measure  the  Angle  of  the  Prhm.—{\)  By  Mocimj  the 
Telescope.— li  the  adjustment  for  the  parallelism  of  the  in- 
cident light  has  been  carefully  carried  out,  no  groat  care  need 
be  exercised  in  centering  the  angle  of  the  i)rism  in  question 
on  its  table. 

Turn  the  prism  table  so  that  its  vernier  may  be  out  of 
range  uf  the  moving  telescope,  and  clamp  it  down. 

T'M-n  th.    -rism  on  its  table  till  the  angle  to  be  measured 
points  tow      s  tlje  slit,  and  clamp  it  in  position. 

Illuininat:^  the  slit  ^'ither  by  the  sodium  flame  or  bv  turn- 
ing  the  insf      uent  so    imt  the  collimator  points  to  a  window. 
-  i^'ope  to  view  the  reflection  of  the  illuminated 
''   '  faces  wliich  bound  the  angle  in  question. 
?  as  narrow  as  possible,  and  adjust  the  position 
by  'he  tangent-screw  attached  till  the  vertical 
38  with  the  middle  of  the  slit. 
Read  the  ^«^      -n  of  the  telescope  on  the  graduated  circle. 
Turn  the  tek         "to       w  the  slit  from  the  other  face  of 
the  angle,  reading  tt=        ^itior,  of  the  telescone  as  before. 


Turn  t 
slit  from  t 

Make  tb. 
of  the  telescoj 
cross -wire  coin 


90 


LA  BORA  roii  r  rnrsTcs. 


llnclamp  the  prwm  tttl»le,  set  it  again,  luid  rtpout  flie 
uhHcrvatioiiri. 

Tiie  im-aii  (iiJTert'iuH!  between  the  reudin^s  on  the  two  sides 
of  tlie  pribHi  in  t*  he  taken  an  twice  the  angle  refpiired. 

Ditticulty  may  lie  exiHTieiiced  at  tinst  in  tinding  tlie  reflec- 
tion  of  the  slit  on  the  faces  of  the  prism  hy  looking  through 
the  telescoiKJ.  It  may  easily  he  found,  however,  with  the 
naked  eye,  and  the  telescope  then  moved  up  till  the  image  in 
intercepted. 

(2)  lii/  Moiu'/Kj  the  I'rixHi. — It  will  generally  he  necessary 
to  change  the  position  of  the  prism  on  its  tahle  so  that  when 
the  slit  is  in  view  on  one  side,  tlie  vernier  carried  hy  the 
prism  tahle  is  as  near  as  iHJssible  to  that  carried  by  the 
telescope. 

The  observations  will  be  taken  in  the  same  way  as  before, 
except  that  the  i)rism  table  will  be  moved  instead  of  the  tele- 
scope, and  the  readings  taken  at  the  vernier  carried  by  tlie 
prism  table. 

The  telescope  should  be  displaced  a  little,  and  the  readings 
repeated. 

To  Find  the  Index  of  Refraction  of  the  Prinin.—lt  w'll 
be  necessary  in  this  experiment  to  liave  the  slit  illuriiinaiod 
by  the  sodium  flame. 

Remove  the  prism  and  turn  the  telescope  to  view  the  slit 
directly  through  the  collimator. 

Set  the  telescope  so  that  the  vertical  cross-liair  coincides 
exactly  with  the  nnddle  of  the  slit,  and  read  the  i)08itlon  of 
the  telescope  on  the  graduated  circle. 

Replace  the  piism,  and  turn  the  telescope  so  as  to  view 
the  refracted  image  of  the  slit. 

To  Determine  the  Minimum  Deriuiion,  de«!rease  the 
angle  of  incidence  by  turning  the  prism  tal)le,  and  follow  the 
refracted  ray  with  the  telescope  till  a  point  is  reached  where, 


^f:^'j^:^jy^^: 


Liairr. 


91 


if  the  prism  be  turind  fmth.r,  tl,,    ivfrncfcd  ray  turns  harlc. 
Head  tho  ))(>8itinn  of  tlu;  t«>lt'Hc.)jM-. 

Tin;  (lillert'lice  Uctwt'tii  this  und  t!ic  h  ..ucr  reading  i,.  tl.c 
angle  required,  JJ. 

Eeniove  ihe  prism,  displace  the  culiimator,  and  readjust 
the  telescope  to  view  the  slit, 
llead  the  vernier. 

Kei)lace  the  prism  and  take  a  Kect.nd  ohservatio.i  fur  min- 
inium  deviation. 

Take  a  mean  of  the  two  ohse.  .ations. 

It  would  he  well  U,  check  the  result  hy  reversing  the 
prism,  8o  that  the  face  of  incidence  is  made  that  of  refraction, 
and  measuring  the  deviation  in  the  opposite  direction. 

Calculate  the  refractive  index  from  the  known  angle  of  the 
prism  and  its  mininmm  deviation  hy  means  of  the  formula 

sin 

M   =  r 

sm  - 


Example. — Enter  results  thus 


Movin);  Telescope. 


Reading  i  ReadiiiK 
KiRlit.    j      Left. 


150""  56';   31"  10' 

157    (HY   37"  15' 

Meau 


Mi)viii){  Prisni. 
Hitclit.      Left. 


I      For  Mininiiiiii  Ueriution. 


59°50'ii:4°10'!54''25''59°5a' 
59°  52'  ;17rj.T|5r  40'  5!»'  52' 

5!»°5r~j  ,-)»"  52' 


TliriiiiKii    rtit'OUKb 
Col.     I   Prism. 


91°  0' 

90°  35' 
_____ 


41"  45' 
41°  20' 

49"  15' 


1.66 


I  MoviiiK  Telescope. 

Rt-adinit  |  Reading  I 
Rijtlit.    ,      l.eft. 


Mean . 


Ma  Ilk  fo  hi-p'JIcil  In  hi/  .student 

Movin»{  Prism. 


For  Minimum  Deviation. 


HiKlit. 


I^-ft 


Throiigl 
Col. 


D 


Through 
Prism. 


.if.X-^Tras 


92 


LABOSATOSY  PliYSlva. 


■c, 


c 

Fig.  22. 


31.  TO  DETERMINE    THE  REFRACTIVE    INDEX   OF  A 
LIQUID  BY  MEANS  OF  A  MICROSCOPE. 

References.— Watson,  p.  495. 

Apparatus  Required.— A  microscope;  a  beaker  with  a  fine 
cross  or  other  well-defined  object  at  the  be  toni ;  a  fine  milli- 
meter scale  for  detennhiing 
the  positions  of  the  micro- 
scope tube. 

Theory  of  Experiment 

If  an  object    C  placed  in  a 

vessel  partially  filled  with  a 
liquid  (e.g.,  water)  be  viewed 
from  a  position  perpendicu- 

larly  above  the  liquid,  it  will 

appear  at  a  point  C,  nearer 
the  surface   than   C,  due  to 
the  refraction  of  the  liquid. 

If  A  be  the  point  on  the  surface  of  the  liquid  perpendicu- 
larly above  C,  then  the  refractive  inde.x  of  the  liquid  is  given 
b}'  ecjuation 

ACf 

^  =  Ac; 

In  order  to  measure  the  distances  AC owik  AC„  a  micro- 
scope can  be  used  as  follows. 

Practical  Directions — Scratch  on  the  bottom  of  a  beaker 
whicli  is  at  least  two  inches  high  a  fine  cross. 

Place  the  beaker  under  the  object-glass  of  the  microscope, 
and  carefully  focus  on  the  cross  at  the  bottom. 

Measure  with  a  fine  scale,  to  ^V  of  a  milUmeter,  the  distance 
between  a  fixed  point  on  the  microscope  and  a  fixed  point  on 
the  stand. 


LIGHT. 


93 


Denote  tin's  distance  by  S. 

The  focussing  and  measuring  sliould  l)e  done  tliree  times, 
and  the  mean  position  of  the  tube  taken. 

Pour  in  some  liquid  and  sprinkle  some  light  powder,  such 
as  Ijcopodium,  on  the  surface. 

Now  focus  on  the  refracted  image  of  the  cross,  and  again 
measure  carefully  the  distance  between  the  two  fixed  points,  6  . 

Take  a  mean  of  three  observations. 

Then  focus  on  the  lycopodiuni  powder  on  the  surface, 
taking,  as  before,  a  mean  of  three  observations  of  the  distance 
between  the  points,  rf,. 

The   depth  AQ    of  the  liquid  is   clearly  the  difference 
between  the  tiret  distance  and  the  last,  d  -  rf„  and  the  length 
AC,   the  difference  between  the  second  distance  and  the  last 
<y.  -  tf,. 

Deduce  these  lengths  and  calculate  tlie  value  of  /<  from 
formula  (1). 

Example. — Enter  results  thus : 


7.57 
7.57 
7.58 


«. 


6.70 
6.69 
6.69 


«, 


4.06 
4.06 
4.05 


AC 


3.51 
3.51 
3.53 


AC, 


2.64 
2.63 
2.64 


Mean  value  of//. 


Blnnl' to  h'^iiUetl  h)  hn  Hfudent. 


AG 


AC, 


Mean  vsliip.  of  //, 


1.330 
1.335 
1.337 


1  334 


HEAT. 

32.   TO  CONSTRUCT   AND   CALIBRATE  A  SPIRIT   THER- 
MOMETER. 

References.-I'reston,  p.  ir,4;  Nichols  aiHl  Franklin,  v,.l. 
I.  p.  ir,H;  Ames,  p.  2(»7;  Knott,  p.  214;  IWkor,  p.  272: 
Hastings  and  Bead.,  p.  175;  Antlionv  and  Mraekett,  i).  206- 
Watson,  p.  279.  '  '  i  » 

Apparatus  Required.-A  -lass  tnbe  cf  abont  i  mm.  In.re 
witlj  a  hnlb  blown  on  one  end;  some  alcohol;  a  j^la^s  beaker; 
a  small  tripod,  with  iron  -anze  cover;  a  bnnst^i  bnrner;  a 
vessel  filled  with  siiow  saturated  with  water;  a  suitable  funnel 
for  tilling  bulb. 

Theory  of  Experiment. -If  the  -lass  bulb  be  iillea  with 
alcohol  or  other  li.p.i,].  and  heated,  the  li.pii.l  will  expand  and 
rise  in  the  tube  c.nnected  to  the  bulb.  The  expansion  will 
be  proportional  to  the  increase  of  temperature,  or 

F=i:(i  +  ^/), 

where  i;  is  tlie  volume  at  zero  tenii)erature,  and  V  that  at 
temperature  f.  The  increase  of  temi)erature  mav  therefore 
l)e  measured  by  nu-asurin-  the  rise  of  the  liquid  in  the  tube. 
The  tube  can  thercf..r«.  (assuming  the  uniformitv  of  the  bore) 
be  calibratc.l  in  de-rees  of  ten.peratui-e  by  deterun-niniv  t],c 
positwn  of  the  H.p.id  f„r  two  difterent  temperatures  and 
(hvidinir  it  proportionailv. 

M 


rm 


svai:.  vff^xKS!i^,^TCsr^mamBie3i:iis3.'7WSfjsBKBr:^^.  «^ihw.^  .vi^BBsrspfflapgraqisffEaiiHigii'aijagMBBMiirfiw! 


-i 


HEAT. 


95 


Practical  Directions.— Blow  a  suitable  hnlb  on  the  end  of 
the  tube.  For  4  mm.  bore  the  bulb  should  be  about  1 
cm.  diameter,  the  tube  being  about  i  of  a  meter  in  length. 

Connect  a  small  glass  funnel  to  the  end  of  the  tube  to  be 
filled,  by  means  of  a  rubber  tube  fitting  each  tightly. 

J'artially  fill  tiie  funnel  with  alcohol. 

Kow  gently  heat  the  bulb  over  the  gas- flame  thus  expelling 
the  air  from  the  bulb. 

On  cooling  the  bulb  it  will  ])e  found  partially  filled  with 
the  licpiid. 

Now  gently  boil  the  liquid  till  it  is  expelled,  and  again 
cool. 

The  bulb  will  now  be  found  to  be  full  of  liquid,  with 
probably  the  exception  of  a  .small  air-bubble  in  the  top  or  in 
the  stem.  To  get  rid  of  tliis  final  bubble,  hold  the  tube  in 
the  hand  with  the  bulb  downward,  and  swing  it  with  a  circu- 
lar motion.  The  air,  being  iightei-,  will  l)e  displaced  by  the 
li<]uid,  due  to  its  greater  (-(Mitrifugal  force. 

By  cotitinning  this  action  the  air-bubble  can  be  made  to 
rise  in  the  tube,  and  can  finally  be  expelled  by  slightly 
warming  the  bulb  with  the  hand  or  iti  warm  water. 

Seal  the  tul)e  by  means  of  a  l)lowpipe  flame. 

To  accomi)lish  this  easily  the  tube  should  ])e  drawn  out  at 
:;he  point  for  sealing  before  it  is  filled. 

Warm  the  li(piid  till  the  tube  is  just  full  to  the  sealing 
point. 

The  sealing  should  be  doTie  quickly,  and  the  bulb  cooled 
at  once  to  permit  the  liquid  to  contract. 

If  alcohol  be  used,  it  should  be  at  about  75°  when  sealed, 
so  that  a  good  range  of  temperature  can  be  obtained. 

This  can  l)e  accomplislie<l  by  keei)ing  the  bulb  in  the  glass 
beaker  filled  with  water  heated  to  about  75°  C. 


'AUKr,44-^<'»t-^  ';*i!--.V,*'."^Tr-'*' ;' '. 


"a?i??s»«K:^!ip«iSffi"KiaE.'i'.-'f>" 


96 


LABOliATORY  PHYSICS. 


As  tlie  boiling-point  of  alcohol  is  about  79°  C,  the  ther- 
mometer must  not  be  heated  to  that  point. 

Now  fasten  the  bulb  and  tube  to  a  narrow  strip  of  section- 
paper.  Determine  the  zero-point  by  p,,ttin<r  the  bull,  in 
Buow  saturated  with  water. 

Determine  a  point  at  say  r.«.°  or  :(•''  by  licatin.i,.  it  in  water. 

To  do  this  a  mercury  thermometer  must  be  used,  and 
simultaneons  readings  taken. 

Divide  the  secti<ni-paper  into  degrees  of  temperature. 

This  experi.nent  recpiires  considerable  skill,  and  the  stu.lent 
must  not  get  discouraged  if  he  fails  on  tirst  trial. 

Eeturn  the  thermometer  with  your  name  written  on  it 


33.   TO  TEST  THE  FIXED  POINTS  OF  A  THERMOMETER 
AND  TO  DETERMINE  THE  STEM-EXPOSURE  COR- 
RECTION  FOR  ANY  TEMPERATURE. 

References—Preston,  ,,.  105;  Watson,  p.  210;  Barker 
p.  273;  Anthony  and  Brackett,  p.  189;  Hastings  and  Beach' 
p.  165;  Ames,  p.  202;  Knott,  p.  195;  Nichols  and  Franklin' 
vol.  I.  p.  151,  ' 

Apparatus  Required.— A  thermometer  to  be  tested-  a 
telescoi^e  for  accurately  reading  the  thermometer;  a  -laJs 
beaker  filled  with  snow  saturated  with  water;  u  hvi)sonreter 
ami  suitable  burner. 

Theory  of  Experiment.-(l)  \^y  testing  the  fix-c.l  p„ints  of 
a  thermometer  is  meant  the  determination  of  the  indications 
of  the  thermometer  corresponding  to  the  freezin<r-point  of 
water  and  to  the  boiling-point  of  water  under  700  mm.  pres- 
sure. Suppose  on  reading  the  freezing-point  it  is  found  not 
to  be  the  imlicated  zero,  but  to  differ  from  i'  bv  a  small  value 


rWJi^i  *>7KWftK0aSIRai  «■ 


i 


HEAT. 


t>7 


±  a,  a  beinj?  considered  plus  wlien  the  reading  is  above  tlie 
zero,  and  minus  when  below. 

If  when  the  boiHng-point  is  observed  the  I  ironietrie  read- 
ing differ  from  700  mm.  by  i.,  then  the  true  temperature  of 
the  steam  is  1()(»  ±  (/>,  x  .<';iT),  according  as  the  barometric 
reading  is  greater  or  less  than  7(3()  mm. 

Suppose  the  reading  on  the  thermometer  to  differ  from 
this  true  value  by  a  small  fpiaiitity  ±_  i,  />  beim;  +  or  — 
according  as  the  thermometer  reading  is  al)ove  or  below  the 
true  reading.  Then  the  total  error  in  the  length  of  the  stem 
for  loo  degrees  of  temperature  is  ±  f«  :i:  h. 

Hence  a  true  degree  on  the  thermometei-,  supposing  the 

10(»  ±a  ±h 


1(»0 


tube  to  be  uniform  in  bore,  is  indicated  l)y 
divisions  of  the  thermometer,  and  therefore  any  temperature 
t  would  be  indicated  by  J"-  ± /'.  ±J  ^  t  thermometer  divi- 
sions from  the  true  zero,  or  from  the  zero  of  the  thermometer 

100  ±a±l 


100 


y.  t  ±a.  . 


0) 


'  I 


(2)  If  when  the  boiling-point  is  observed  the  thermometer 
be  wliolly  immersed  in  the  hypsometer  and  the  reading  taken, 
and  the  observation  repeated  with  30  or  4(»  degrees  of  the 
stem  exposed,  it  will  Ijc  found  that  the  readings  slightly  differ, 
(.wing  to  the  exposure  of  the  stem  to  the  air.  Denoting  the 
length    of    stem    exposed    by   d\    and   the  difference  \\\  the 

readings  by  l-,  then  the  stem  correction   i)er  dca-ee  is  — 

Th"s  stem  correction  will   depend   not   only   on   the  stem 
exposed,  but  also  on  the  temperature  being  determined;  and 


fms^^siiS!m»iimifig. 


*  >■:-•  tft"if3IBSJ-aii^-Ti;"  13  Jt-'JC  -TWfc-.C**-'  •TigSSttS*'!:- 


U8 


LAUOHATORY  J'HiSJCS. 


will  be  positive  or  negative  according  as  that  temperature  is 
above  or  below  the  temperature  of  the  room. 

The  reading  of  tiie  thermometer  eorre6])onding  to  any 
temperature  t  k  therefore 


!(»(»  ±a  ±h  Xr?, 

(Ther.  reading  :f  <<  T-f-')  100 


or 

I- 


t  = 


(-^) 


(3) 


100  ±a  ±b 
^  being  the  stem  correction  for  tenjperature  t,  and  <5,  tlie 

length  of  stem  exposed  when  the  temperature  t  is  taken. 

Practical  Directions.— Insert  the  thermometer  in  the  mix- 
ture of  snow  and  water,  leaving  oidv  sutticient  of  the  mercury 

CD  ti  ^ 

column  exposed  to  enable  you  to  take  the  reading. 

Head  by  means  of  the  telescope  the  indication  of  the 
thermometer  to  yjg^  of  a  degree. 

This  reading  gives  y(»u  the  value  a. 

I>y  moans  of  a  8])lit  cork  insert  the  thermometer  in  the 
hypsometer,  and  let  the  steam  How  freely  for  a  couple  of 
minutes. 

As  before,  have  only  sutticient  of  the  stem  exposed  to 
enable  yon  to  take  the  reading. 

Read  the  indication  again  as  above. 

Read  the  barometer,  and  calculate  the  true  temperature 
of  steam,  or  find  it  from  a  chart  in  the  laboratory. 

The  difference  between  this  and  the  thermometer  read- 
ing gives  the  value  h. 

Now  expose  the  stem  40  or  50  degrees  and  read  the 
therinometei'  again. 

Calculate  the  stem  correction  per  degree  of  stem  ex- 
posure. 


•  i^wff-^'  :r"  ;'^'".^*^jse$'^ss^*' 


-SMfiS^t'^c^fe'^T 


HEAT. 


S»9 


("alculute  the  teinpcratnre  corresponding  to  a  reading  of 
•io  (li'grc'L's  on  the  tliennoniuter,  isni»po8ing  you  can  uegleut 
tiio  .stem  (•onx'ction. 

Kind  tlie  temperature  by  tlie  thermometer  of  the  solu- 
tion  provided,   and  calculate  the  true  temperature. 

Example — Enter  results  thus: 


a 

liaroiiifter 
Rfiiiliiil,'. 

OIiMilated 

Teiiipf'i'aliire  of 

Steam. 

01)Sfrve(i 

TennxTatiirc  of 

Sleaiii. 

b 

76.3 

100.11 
4 

100.70 



1  f  iiiptratuif  of 

SSolution  hy 
Tliermonietfr. 

+  .59 

Tlwr.  Ki'UiliiiK, 
no  sicm 

Thfi-.  R<'!uliiiK. 

•Jll"  ^telll 

•  xposiiii'. 

Coi  rected 
TeiiipHrature. 

lOO.TO 

10()..50 

.01 

42.30 

4'2.76 

Bhdtk  to  hep'lhd  In  hij  Ktu(h-7lt. 


a 

IJaroMiPter 
Rending. 

Caleidiited 

Teinpenitiire 

of  Steam. 

Oliserved 

Teiiii>erature 

of  Steam. 

b 

Tlier.  ReadiuK, 
no  stem 

exposed. 

Ther.  Reading. 
•i(y  stem 
exposure. 

k 
i 

Tempeiatiiie  of 

Solution  by 
Tliernionieter. 

Corrected 
Temperature.  ; 

1 

''^^'m-^?'ms^^\'i4^s^''iL'mms:^'X9^-f^- 


^*«!  ^=5^,itq?lgv, 


100 


LABORATORY  PHYSICS. 


34.   TO  DETERMINE  THE  COEFFICIENT  OF  EXPANSION 
OF  A  LIQUID  BY  A  WEIGHT  THERMOMETER. 

References. — Carhart,  pt.  11.  p.  30;  Preston,  p.  173; 
Knott,  pt.  I.  p.  214;  Aines,  p.  207;  ^Nichols  and  Franklin, 
vol.  I.  p.  153;  Hastings  and  Beach,  p.  169;  Antliony  and 
Brackett,  p.  208;  Barker,  p.  291;  Watson,  p.  219. 

Apparatus  Required. — A  weight  tliermonieter ;  a  hyj)soin- 
eter  with  suitable  stand  for  use  with  hunsen  burner ;  a  bun- 
sen  burner;  a  beaker;  athernioineter;  a  small  flip  for  holding 
weight  tlieruionieter. 

Theory  of  Experiment. — If  a  glass  tube  be  filled  with 
glycerine  or  other  liquid  at  a  temperature  t,  and  then  heated 
to  another  temj)erature  ^,,  the  li(|uitl  will  expand  and  part  of 
it  will  be  expelled  from  the  tube. 

Let  Y^  denote  volume  of  the  tube  at  the  teinj)erature  /; 
K,  that  at  the  temperature  /, ; 
F,  the  total   volume    of   the  ex2)andod  glycerine  at 

temperature  t^ ; 
6^  the  density  of  glycerine  at  t ; 
tf,  the  density  at  /, ; 

a  the  coefficient  of  the  expansion  of  the  glass ; 
ft  the  coefficient  of  the  expansion  of  the  glycerine; 
J/,  the  mass  of  liquid  in  the  tube  at  t', 
J/,  the  mass  in  the  tube  at  temperature  ^,. 
Then  the  following  relations  hold : 

T^,«y,  =  3/"„; (1) 

FA  =  J/.; (2) 

T^o^^o  =  M, ; (3) 

r,  =  F,  |i  +  ^r^,  -  t)\.     ...   (4) 

Hence,  comlnning  (1),  (2),  and  (4), 
S.       J/„ 


.V, 


*(^  -0:. 


(5) 


>  ..,^^Sr-:S'^s::TE^A^'Ts^mM£^^'^SLnt^Li£Myt'^^£Li^-iUajarir^Ksv9^^^'s^ 


tZZfJ'M  .  »S1  ^.  SL^Mil3L5Jc:^CSSIWV^.jS:it  1  1 


iiBA  r. 


101 


Also 


and  therefore 


Hence 


But 


V. 


r,  -  \\ 

r.(^-/) 


J/,  -  J/.  ^  J/. 


(«) 


=  /^, 


the  coefficient  of  expansion  per  \init  vohime  per  degree  of 
temperature.      Hence 


(7) 


from  which  ft  can  he  calculated  if  oc  he  known  and  the  otiicr 
values  ohservetl. 

Practical  Directions. — A  s-ntal>le  weiirht  thormonietor  can 
ho  made  from  a  piece  (»f  glass  tuhe  1  cm. 
diameter,  drawn  out  as  in  Fig.  23.     The 
hulh  AB  should  he  ahout  7  cm  long. 

Weigh  it  carefully  to  .()(»1  gm.,  deno- 
ting the  weight  l)y  If. 

Fasten  the  thermometer  in  the  clip 
for  the  purpose,  and  adjust  the  vessel  eon- 
taimng  glycerine  till  the  end  of  the  fine 
tuhe  of  the  weight  thermometer  is  im- 
mersed in  the  glycerine. 

Now,  hy  means  of  a  hunsen  hurner, 
slowly  heat  the  glass  hull),  thus  ex{)elling 
some  of  the  air  hy  expansion.  vw.  23. 

Let  the  hull)  cool,  and  on  eooling  the  glycerine  will  rise  in 
the  tuhe  and  partially  fill  the  hiiib. 


10'2 


I.AIUUtA TOR Y   ril YSK 'S. 


Again  hlowly  heat  tlu;  l»ull»  until  tliu  jilycrrinu  Wegins  to 
boil  and   again  cool,  rcjHJiiting  the    operation  until  tlu*  In 
bubble  of  air  is  expellcil. 

Keeping  the  end  of  the  tube  still  under  the  gl\  ferim-,  ftu 
the  bulb    to  about    1°  above   the  teniperuture  of  tlie  rouui. 
This  can  be  done  by  putting  the  bulb  in  a  beaker  of  water 
slightly  wanner  than  the  room  temperature. 

The  glycerine  nuist  be  left  for  tiome  minutes  in  the  water 
to  secure  uniform  temperature,  the  water  being  slowly  stirred 
with  the  thermometer  all  the  time. 

Read  the  temperature  of  the  water,  t. 

Kow  take  the  weight  thermometer  out  of  the  water  and 
carefully  dry  with  a  cloth,  being  careful  not  to  Jieat  it  with 
the  hand  or  the  glycerine  will  expand  and  some  of  it  lirop 
from  the  tine  tube.  On  taking  it  out  of  the  water  '  •>  the 
cooler  atmosphere  of  the  room  it  will  slightly  contr;  ,  thus 
making  it  possible  to  weigh  it  without  loss. 

Weigh  carefully  tlie  now  tilled  bulb  again  to  .(lol  gui. 

Denote  the  weight  by    IT,. 


TF.  -  W  =  M,. 


Now  suspend  the  weight  thermonieter  inside  a  liypsometer. 

Tliis  can  easily  be  done,  if  the  bulb  lias  been  properly 
made,  by  having  a  split  cork  for  the  top  of  the  hypsometor. 

Allow  the  steam  from  the  liypsotncter  to  flow  freely 
around  the  bulb. 

If  it  be  not  convenient  to  use  a  hypsometer,  the  bulb  can 
be  suspended  in  boiling  water,  and  the  temperature  of  the 
water  taken  with  a  thermometer. 

If  the  hypsometer  be  used,  read  the  barometer  and  take 
the  temnerature  f,  from  the  chart  in  the  room. 

The  overflow  of  glycerine  should  be  caught  in  ;i  beaker. 


UICA  T. 


l(t:5 


U'jive  the  bull)  in   the  hypsoiu.   or  or  water   until   the 
glycerine  ceawes  to  drop  from  tlie  ojhji   end  of  the  tube. 
Weigh  again. 
Denote  the  weight  by   11',. 

J/.  =  »;  -  ir; 

a,  for  glass  =  .00002»'». 
Subfltitute  these  results  '     *''*^  furnni'H    a!id  calculate  ft. 
Example. — Enter  resuh  -: 


w. 

W,. 

1 

10.670 

17.875 

6.H06 

n.18^ 


"'.• 


Afu< 


lilnnktvt^  itJltd  i     f>y  ^ '>></<  ut. 


M 

'.. 

\ 

ij.tm 

^.7 

.(Kmw! 

i((li  lit. 

.w, 

'.. 

n. 

35.  TO   DETERMINE    THE    Cfs       ICTENT    OF    LINEAR 
EXPANSION  OF   ilRASS. 

kef erences.— Watson,  p.  214;  Prest..  .  p.  98;  Hastinfrs 
and  Beach,  p.  172;  Carhart,  pt.  ti.  p.  ?> ;  Barker,  p.  2S9; 
Anthony  and  Braclcett,  ]».  208;  \iehols  and  Franklin,  vol.  i. 
p.  153;'  Ames,  p.  204;   Knott,  p.  217. 

Apparatus  Required. — Two  microscopes ;  two  brass  tubes, 
one  considerably  larger  tlian  the  other;  a  hypsometer,  with 
rubber  tubing  to  make  connections ;  a  l)eam-compass ;  a  centi- 
meter scale;    two  thermometers. 


•)t 


L  A  noli,  t  ran  y  rii )  sk  -s. 


Theory  of  Experiment If  u  hra^s  rod  of  len^'fli    /   and 

tiiiitunii  tiiinicrHtiiio  /  Ikj  licuttHl  until  it  iittuiiiH  ii  unifMi-iu 
U'liiporuturo  /,,  it  will  bo  found  on  nuasuiTUient  to  liuvo 
incrt'iisnl  in  lenj;th. 

Denote  tin- liMiuth  at  ti'mperafnie  /,  l>y /,.  The  coetlii-ient 
of  linear  e.\pan>ion  between  /  and  /,  is  given  !)}•  the  e(|uation 

whore  n  is  the  coetHcient  of  linear  expansion. 

If  /  and  /,  he  niea«jured,  t  and  i,  observed,  a  can  he  cal- 
cnlati'd. 

Practical  Directions  — I>y  menus  of  cork.s  in  the  ends, 
arrange  tlie  smaller  tu.<  UKiide  the  larger  one  as  in  Fig.  24. 
CD  is  the  siiiall  tul>e,  tne  eoetlieient  of  whieh  is  to  be  deter- 
M  N         . 


^-~ 

A 

B- 

ks^ 

a — 

") 

l, 

^J 

Fio    'J4. 

nuued.  A  and  ^  are  small  glass  tubes;  aa„  Ji,,  thermom- 
eters. AVi'  is  a  rubber  tube  eoiiuecting  the  iut<:ide  of  the 
inner  tube  C'/)  with  the  inside  of  the  outer  tube  MN.  />J* 
i-  a  ruliber  tube  eonneeting  the  liypsoineter  to  the  inner  tube; 
/A,,  a  rubber  tube  for  eun-ying  otf  the  steam  as  it  flows  out 
of  the  enter  tube. 

iviake  two  sharp  knife-cuts,  ('  and  />,  at  places  in  the 
outside  portion  of  tlie  inner  tube,  convenient  for  observations, 
yet  as  close  as  possible  to  the  corks  in  the  large  tul>e  iJ/iV. 

Focus  one  of  the  mierosc(';>e8  on  the  cut  C' and  adjust 
until  the  cross-hair  of  the  microscope,  being  central,  is  over 
the  centre  of  the  cut. 


UK  AT. 


105 


Clump  tlie  microscope  to  the  tulde  or  ulah  on  which  tlie 
appHratus  U  placcMl. 

Siinilurly  adjust  the  other  iiiicro8Coi>e  to  tlie  cut  I). 

Head  carefully  the  temperatures  of  the  thermometers 
inside  the  tube,  and  take  the  mean  of  the  two  as  t. 

Lij^ht  the  burner  under  the  hypsometer  and  let  the  steam 
flow  freely  throu<;h  the  inner  tube,  outer  tube,  and  again  to 
the  air. 

Let  the  steam  tlow  freely  for  a  few  minutes  till  the  temper- 
ature becomes  steady. 

Read  the  barometer,  and  tin;  temj)eniture  of  the  steam 
corresponding  to  the  barometric  pressure  from  the  chart  in  the 
laboratory. 

On  lookini;  through  the  niicros('o|K's.  it  will  be  found  that 
the  cuts  on  the  tube  have  now  moved  away,  one  to  the  right 
and  one  to  the  left  of  the  cross-hairs. 

Count  the  number  <  f  niicronieter  divisions,  in  each  case, 
between  the  cross-haira  and  the  new  p<»sitiiins  of  the  cuts. 

This  may  be  done  by  counting  the  scale  divisiojis  in  the 
micro6C(»pe,  or  by  counting  the  number  of  turns  of  the  microm- 
eter head,  in  each  case,  retpiired  io  move  the  cross-hairs 
from  their  origliud  positions  to  the  new  positions  of  the  cuts. 

The  sum  of  the  two,  expressed  in  centimeters,  gives  the 
expansion  of  the  rod. 

Now  measure,  by  means  of  a  tine  scale,  the  value  of  each 
micrometer  division. 

This  can  be  done  by  focussing  the  microscope  on  the  tine 
scale,  the  divisions  of  which  are  known,  and  ccuuting  the 
micrometer  divisions  corresponding  to  a  scale  division 

The  cxpai;sion  /,  —  /  is  thrs  deteri.iined  in  centimeters. 

Now  measure,  by  means  of  the  beam-compass  and  a  centi- 
meter scale,  the  length  /  to  the  nearest  millimeter. 

Calculate  a  from  formula  (1). 


ffi 


106  LABORATORY  PHYSICS. 

Example.— Enter  re8iilt8  thus: 


« 

'. 

80  0 

li>.5 

99.5 

Microiiieter;Microiiieter 
Oivixiuus  lu  Divitiionsiu 

RiKht  Left 

Micruocopf.  j  Microscope. 


6.5 


6.2 


/, -/ 

I 

a 

.oooo 

.147 

100 

184 

Blank  to  he  Jill ed  in  hy  student. 


t 

t, 

t,-t 

Micrometer 
Divisions  in 

KiKiic 
Microacope. 

Micrometer 
Divisiuus  in 

Lfft 
Mici'uscupe. 

1,-1 

I 

a 

J    i 


36.  TO  DETERMINE  THE  COEFFICIENT  OF  INCREASE 
OF  PRESSURE  OF  AIR  BY  MEANS  OF  A  CON- 
STANT-VOLUME AIR-THERMOMETER. 

References. — Xicliols  and  Franklin,  vol.  i.  p.  146;   Ila'^t 
ings  and  Beach,  pp.    164  and   1S2;  Carhart,  pt.   i,  p.    30; 
Anthony  and  Brackett,  pp.  191  and  222;   Preston,  ])p.  12!> 
andls7;   Knott,  p.    211;    Ames,  p.  212;   Barker,  p.   295; 
Watson,  p.  229. 

Apparatus  Required — A  constant-volume  air-thermometer ; 
a  nietal  vessel  for  snow  and  water  mixture;  a  hypsometer;  a 
hunsen  burner;  a  telescope. 

Theory  of  Experiment — Lot  V„  he  the  volume  of  a  mass  of 
gas,    ¥,    at  0°C.  or  T,  of  the  al)sohite  scale,   and  under  a 


IIKA  T. 


107 


pressure  /*, ;  F,  '1\  ■\- 1,  uiid  1'  the  corresponding  values  when 
volume,  pressure,  and  temperature  change.  The  law  connecting 
the  two  sets  of  vahies  for  the  same  mass  is  given  hy  the  formula 


P  V 


0     '    0 

y— 


PV 

If  the  volume  be  kept  constant, 


=  MK. 


(1) 


,     or    T,=  -B 


p: 


If  the  pressure  be  kept  constant, 


5_       ^         or    7^--^^ 

If  a  be  the  coetticient  of  increase  of  pressure  at  constant 
volume, 

-  1'  -  ^»  -  i    -  ^  -  ^*  (^^ 

"-     pjt     ~  7;  ~     V,t'  '    '    •    ^^) 

Hence  the  coefficient  of  iiicrease  of  pressure  at  constant  volume 
is  equal  to  the  coefficient  of  increase  of  volume  at  constant 
pressure. 

The  fonnula  for  the  present  experin^ent  is 


P  -  P. 


a  = 


PJ 


(3) 


In  the  actual  working  of  the  exi)eriment  there  are  two 
corrections  which  nnist  be  a]>plied.  which  introduce  additional 
terms  in  the  fornuda.  These  will  be  discussed  under  next 
section. 

Practical  Directions. — We  shall  assume  that  an  air-ther- 
mometer of  the  Jolly  type  is  used. 


M^^- 


•  i' 


im 


mi. 


I 


■¥i 


5! 


i    !' 


108 


LABORATORY  PHYSICS. 


Ohsermti&ns  for  Freest ng-jmiit.—lhe  bulb  of  the  ther- 
iHoineter,  liuviiig  been  filled  witii  dry  air,  should  be  first  care- 
fully packed  in  snow  or  ice  saturated  with  water. 

When  the  temperature  becomes  steady,  raise  the  adjustable 
tube  of  the  manometer  until  the  mercury  in  the  stationary 
one  just  touches  the  black  glass  point  in  the  outer  bulb, 

Kead  the  level  of  the  mercury  in  each  tul)e  by  means  of 
ti.e  telescope  referred  to  the  graduated  scale  attached  to  the 
iiif  trument.  Denote  the  readings  by  A  and  S,  and  the  differ- 
1   ce  of  level  by  jt>„. 

Repeat  the  observations  several  times  and  average  the  re- 

tiUlt. 

Read  the  barometer,  denoting  the  reading  by  //,. 

Observe  the  temperature  of  the  barometer,  ai  also  that  of 
the  air  near  the  air-thermometer. 

If  the  readings  be  nearly  the  same,  the  mercury  columns 
need  not  be  corrected  for  temperature. 

Observations  for  Boil  hif/.pomt.— Insert  the  bulb  of  the 
thermometer  in  the  hypsometer,  and  boil  the  water  by  means 
of  the  bunsen  flame. 

Adjust  the  manometer  as  before. 

Read  again  the  level  of  the  mercun  i  eacli  tube,  denot- 
ing the  difference  by^;„  the  readings  by  ^1,  and  S^. 

Repeat  the  observations  as  before. 

Read  the  barometer,  //,. 

The  barometer  reading  in  this  case  will  not  usually  differ 
much  from  //;,  in  the  preceiling  case. 

The  temperatuieof  the  steairi,  t,  for  the  pressure  //,  may 
be  found  from  a  curve  in  the  laboratory. 

Corrections — In  making  calculations  from  these  observa- 
tions, two  corrections,  as  mentioned  before,  must  be  noted. 

(1)  Correction  for  Krjmnsion  of  the  Glass  Bull. —Tha 
vOiUme  of  air  is  not  tlie  same  in  each  ease  ou  account  of  the 


HEAT. 


109 


expansion  of  the  glass  bulb.     The  relation  between  the  two 
volumes  is  given  by  the  equation 

V=VSl-{-gt),    when    y  =  .000026. 
Since  the  difference  of  temperature  is  nearly  100, 

F=  r.(1.0026) (1) 

(2)  Correction  for  Stem  A'xjwsxre. — The  air  in  the  small 
tube  or  stem  leading  from  the  bulb  containing  the  air  to  the 
tube  containing  the  mercury  remains  api)roxiniately  at  the 
temperature  of  the  room. 

Denoting  the  volume  of  this  small  tube  bv  v,  the  mass  of 
the  air  it  contains  by  ///,  that  in  the  bulb  by  J/,,  we  have  the 
relations 

PV  Pv 

where  T^  is  the  absolute  temperature  of  the  air  in  the  room, 
and  T,  the  absolute  temperature  of  zero  centigrade. 

Since  J/,  +  ^'^  =  ^^  =  constant, 

we  therefore  have 


P  V        Pv 


PV        Pv 


(2) 


The  ratio  of  the  volume  v  to  F",  must  be  determined  if  it 
be  not,  as  in  most  cases,  given  witli  the  instrument. 

Denote  this  ratio  by  ;•.  Substitute  V,r  for  v,  F,(l  +  9^) 
for  r,  and  divide  through  by  V,.     Equation  (2)  now  becomes 


P        rP 


P(l  +  fft)        rP 

■'a 


T.-fi 


i:^. 


^ 


ti 


liO  LAliOHATOItY  I'liYSlCS. 

Multiply  both  sides  l.y       "  ^^     -  »,   take    1  +  ,jt    out    of 
every  term  except  the  first,  iuul  \vc  obtain 

^(1  +  '.ir)T„r  {  rt  r{T„P-(T„+t)l\]  y 

1\  \    ^T^a+yt)^'    JTJ,\+yt)      /• 

Assuming:  TJ*  =  (7;  4-  0/'.  ill  tlie  suuill  term  and 
iH^V'lectiuir  <jt  in  tlie  deiiominatur  of  the  second  term,  whicli  is 
also  small,  we  have 


Ilenci 


(3) 


PJ 


Denotini;  Z;  as  273°  in  the  small  term,  ^„  the  temperature 
cejitiorrade,  and  substitiitin^r  for  1\  and  J\  tlie  values 
^7o  -j-j^o  <in(l  //,  -\-j\,  tlio  formula  becomes 

y^'+^'V^  I  1  +  y^  +  27^^^  -  (^  +7>.)  ]      (4) 


«   z= 


In  the  -lolly  pattern  air-thermometer  used  in  thi>  lab(»ratorv 

_    2..3r> 

'  ~  12472^')  ~  •'^'^'•^*^'  ^''^'  \""l"">e  of  the  stem  per  centhneter 
being  .0227.      In  tlie  Groves  pattern  /•  =  .0150. 

Precautions.— (  n  The  tube  supj.ortinj;  tlie  bulb  is  delicate 
and  easily  broken:  if  must  th<*refore  be  carefully  handled, 
especially  when  packin<i  in  snow. 

(2)  Hefore  takim:  the  bulb  out  of  t'le  hvpsonieter  or 
turiiiug  off  tlic  ^^asHiUne,  lower  tne  adju^iaili(■  tu'iie  of  the 


HEAT. 


Ill 


manometer,  otlle^\vi^se  the  mercury  may  be  forced  into  the 
bulb  as  it  cools. 

(3)  III  the  Jolly  i)atterii  air- thermometer  do  not  touch  the 
three-way  tap  on  the  left-hand  side.  If  this  be  turned  either 
way,  mercury  will  be  spilled. 

(4-)   He  sure  the  hypsometcr  contains  water  before  heating. 

Example. — Enter  results  thus: 

FUEEZlNli- POINT   OBSKHVATIONS. 


76.66 


70.66 


reinptM-atiire 

of 

Bar. 

Manometer. 

v« 

; 

S 

A 

16.2 
16.0 

50.21 
50.21 
50  20 
50.19 

50.53 
50.52 
50.52 
50.51 

0.32 
.32 
.32 
.32 

16.1 

16.1 
16.0 
15.8 

16.1 

50.20 

50.52 

.32 

16.0 

BOILING-POINT  OBSERVATIONS. 

Manometer. 


Temperature 

(if 

Bar. 


"o  =  76.06  +    0.32  =    76.98: 
P,  -^  76.69  +  27.42  ■=  104.11: 
t  —  fpinpernttire  of  steam  under  pressure  76  69  --  100.25; 


104.11  !l.0026  +  ,,,'_;_^;,^- 76.98  I 


a    = 


37^4-  16  4 
76.98  X  100.25 


=     ,003630. 


Illl 


it 


i^ 

1 

-', 

>: 

^ 

« 

I      ' 

4 

■ 

T? 

1^ 

i 

'\t  i 
i4'l   i 


112 


LAliOHATORY  PHY8IV8. 

Blanks  to  If  Jill cd  in  hi/  ntndmt. 
FUEEZING-POIXT  OBSERVATIONS. 


Tem|).  Bar. 


;>■. 


BOILIXU-POINT  OBSERVATIONS. 


I\  = 

r,  = 

t  = 


HEAT 


118 


37.  TO  DETERMINE  THE  COEFFICIENT  OF  INCREASE 
OF  VOLUME  OF  AIR  BY  MEANS  OF  A  CON- 
STANT-PRESSURE  AIR-THERMOMETER. 

References. — As  in  j)recedin<^  experinient. 

Apparatus  Required.— A  siiital.le  glass  hull) ;  a  liypsom- 
eter;  a  bunsuii  hurrier;  a  glass  vessel  of  not  lees  than  S  cm. 
diameter  and  2.')  em.  <lee]»;   a  tlienuonieter. 

Theory  of  Experiment.— It  lias  he  sIk.wh  in  tlie  ex- 
periment on  the  constant-volume  air-thermometer  that  the 
coefficient  of  increase  of  })res.sure  at  con>^tant  volume  is  ecpial 
to  the  coefficient  of  increase  of  volume  at  constant  ])ressure,  or 


rt  = 


PJ 


(1) 


In  the  present  exj)eriment  it  is  proposed  to  keep  tlie  pres- 
sure constant,  and  to  measure  the  coefficietit  by  means  of 
increase  of  volume  from  the  e(|uation 


a  = 


^■^) 


F„  and   T' being  the  volumes  at  (»0.  and  /  respcctivelv. 
If  the  volumes  be  taken  at  ten-.^.eratures  /,  and  /,,  then 


a  = 


r,  -  ]; 


.      (3) 


where  a  is  the  coefficietit  of  increase  of  volume  per  degree  of 
temperature  between  /,  an<l  t,. 

If  a  glass  bulb  of  weight    W  filled  with  air  at  temper- 


114 


LABORATORY  PUYSW8. 


ature  <,  be  immersed  in  water  at  a  temperature  <,  (^,  being 
lower  tlian  <,),  so  tliat  no  air  is  permitted  to  escape,  it  will 
become  partially  filled  with  water,  due  to  the  contraction  of 
the  air  in  the  bulb. 

Denote  the  weight  of  the  partially  filled  tulje  by  If,. 

If  the  tube  be  now  filled  with  water  and  again  weighed, 
its  weight  being  denoted  by  U",,  the  volume  of  the  bulb  at 
temperature  /,  is  obviously 

^K  -  w, 

while  the  volume  when  tilled  with  air  at  temperature  t,  is 
given  by  the  equation 

r.  =  (ir,-  ir)|i +  .000020(^.-^1,    .    (i) 

.000026  beuig  the  coefficient  of  expansion  of  glass. 

The  volume  of  air  F,  in  the  partially  filled  tube  is  ob- 
viously 

TF.  -  W-  (ir.  -W), 


or 

Hence 

a  = 


F.  =  IF,  _  ]r.. 


(2) 


Kit,  -  Q 


(ir,  -  W)]l  4-.000026r^-  0{  -  ( IT,  -  W) 


^  w,-  ir-f-(TT^_  W)imHm(f,-fy. 


.      (8) 


If  Ii;    ir,,   ir,.  be  obtained,  t,  and  t,  observed,  the  value 
of  '»'  can  be  calculated. 


mi  yi 


^  rj^^!^.j^mf 


UEA  T. 


115 


Practical  Directions — A  suitaMe  bulh  for  tlie  experiment 
can  1.U  niiulc  from  a  ])ioce  of  gla««  tube  drawn  out  at  each  end 


as  in  Fi^.  2o. 


Fig.  25 

Make  the  j)firt  .!/>'  ul)out  10 cm.  in  length  fnun  a  piece  of 
tuhe  2  cm.  in  diameter. 

The  buU)  shoukl  i)e  drawn  out  to  a  very  fine  point  at  each 
end. 

Weigh  tlie  hulh,  denoting  tlie  weight  by  IF'. 

Seal  the  tube  at  one  end,  and  by  means  of  a  split  cork 
insert  it,  sealed  end  down,  into  the  hypst.meter,  with  about 
1  cm.  of  the  open  end  protruding  from  tlie  cork. 

Let  the  steam  fiov  freely  for  about  ten  minutes. 

Seal  the  oj^eu  end  by  means  of  a  blowpipe  or  buiisen 
burner.  Kead  the  barometer,  and  find  the  corresponding 
tem])erature  of  steam,  t^. 

Nou  fill  the  glass  vessel,  mentioned  under  apparatus, 
nearly  full  of  water  at  about  the  tem])erature  of  ihe  room! 
Ib.lding  the  end  of  ihe  bulb  under  .va^er,  break  off  a  small 
bit  of  the  top  of  the  tube,  and  immediately  the  tube  will 
become  jwrtially  filled  with  water,  due  to  the  cooling  of  the 
air  and  the  consecpient  change  of  pressure  in  the  bulb.  The 
bulb  should  be  kept  vertical,  open  end  down,  to  prevent  the 
escape  of  the  air. 

The  i)ressure  in  the  Imlb  is  made  up  of  two  parts,  the 
l)ressure  of  the  air  in  the  bulb,  and  the  pressure  due  to  the 
presence  of  acpieous  vapor. 

This  pivssurc  is  e(|ual  to  the  barometric  pressure  plus  the 
dilference  in  the  head  of  the  water  in  the  bulb  and  vessel,  or, 
barometric  pressure  -j-  pressure  of  water  = 

pressure  of  air  -f  a([ueous  vapor  pressure. 


I 


I  ! 
I  ' 


r7i»^ 


116 


LABOliATOliT  PHYSICS. 


i  \ 


Hence  we  can  correct  for  aqueous  vapor  pressure  by  making 
the  preB8ure  due  to  diliercnce  of  bead  of  water  exactly  equal 
to  it,  thus  making  the  pressure  due  to  the  air  in  the  bulb  ex- 
actly equal  to  the  barometric  pressure,  as  was  the  case  when 
the  bulb  was  in  the  hypsometer. 

Calculate,  therefore,  the  depth  of  water  equal  to  the  afpieous 
vapor  pressure  at  the  temperature  of  the  water,  and  depress 
the  bulb  until  a  ditferenco  between  the  surface  of  the  water  in 
the  vessel  and  bulb  equal  to  it  is  obtained. 

In  order  to  ao  this,  read  from  the  chart  in  the  laboratory 
the  pressure  of  the  a(pieou8  vapor  at  tenqierature  of  water. 
Denoting  this  by  /*,  we  have 


A 
13.596 


/',     or 


h  =  P  X  13.596, 


where  A  is  the  ditference  of  head  retpiired,  and  13.596  the  spe- 
cific gravity  of  mercury,  the  vapor  j)ressure  and  baron)etric  pres- 
ure  being  expressed  in  centimotiTs  of  mercury.    While  hold- 
in"  the  bulb  in  the  water  at  depth  A,  seal  the  open  end  with 

wax. 

A  small  piece  of  suital)l(!  wax  can  be  kept  attached  to  the 
bottom  of  the  ve.>;sel  iiit^ide,  and  the  depth  of  the  water  reg- 
ulated so  as  to  give  A  just  as  the  open  end  of  the  tube  touches 
the  bottom  of  the  vessel. 

It  will  be  found  convenient  to  have  a  piece  of  stiff  wire, 
to  use  as  a  handle,  twisted  round  the  bulb. 

Stir  the  water  in  the  vessel,  and  read   the  temperature  t,. 

Kemt)ve  the  bulb,  being  careful  not  to  lose  any  of  the 
water  out  of  it. 

Dry  and  weigh.      Denote  the  weight  by  ir,. 

Now  iill  tlie  bulb  with  water. 

This  can  be  done  by  the  method  employed  in  filling  the 
weighs  ihermometer. 


mm 


BEAT. 


117 


Weigh  the  bull)  wlieii  full  of  water,  (leiiotirig  the  weight 

by  UV 

Substitute  these  weights  in  the  forinulu,  and  euleulute  a. 

Example. — Enter  result^  thus: 


»• 


100.25 

1% 

1*'. 

H, 

« 

10.50 

14.463 

30.268 

.00370 

ill 


Blank  to  he  Jilled  in  hy  student. 

»• 

1, 

(. 

»'. 

"'. 

a 

38.  TO  DETERMINE  THE  SPECIFIC  HEAT  OF  COPPER- 
METHOD  OF   MIXTURES. 

References.— Preston,  pp.  211  and  215;  Carhart,  pt.  n. 
p.  4-t;  Barker,  p.  283;  Anthony  and  Braekett,  p.  193; 
Watson,  p.  288;  Knott,  p.  199;  Ames,  p.  217;  Xiehols 
and  Frankliji,  vol.  i.  p.  Ifi-t;   Hastings  and  Beach,  p.  188. 

Apparatus  Required.— A  regulation  cylindrical  heater, 
with  hypsometer  attach uients  and  calorimeter;  two  thermom- 
eter.'!. 

Theory  of  Experiment.— By  the  specif  c  heat  of  a  sub- 
stance is  meant  the  ratio  of  tlie  quaiitity  of  heat  required  to 


118 


I A  lioiiA  'fun  y  i'ji  YHica. 


raise  tlie  tem|»t'rature  of  u  in.  •»  of  tiie  siil)htanc'e  one  <k'greo 
to  tlie  <jiiuntirv  iiecessHrv  to  raitii'  tin  »'<|ii;il  mii»*s  of  wati-r  one 
degree.  \\y  a  unit  of  heat  U  meant  tin-  4iiatitity  of  heat 
necossary  to  raise  one  gram  of  water  tliroii^'Ii  one  degree. 

If  H  known  niasri  of  «'<»jt[H'r,  ///.  he  heated  to  a  teni- 
perature  /,  and  then  nuddeidy  phinged  info  a  known  mans 
of  water,  J/,  at  a  lower  temperature,  /, ,  and  the  water  stirred 
until  the  water  and  copper  have  a  uniform  ienperature,  t  , 
the  heat  lost  by  the  mass  in  of  eopper  is  ecpiai  to  eii'(t  —  t,) 
units,  where  c  is  the  8i)eciHe  heat  of  copper.  Tiie  heat 
absorbed  by  the  water  is  JI{t,  —  t^).      Hence 


or 


an{t  -  t,)  =  M{t^  -  tX 
M(t,-.  t,) 


e  = 


(1) 


Formula  (1),  however,  takes  no  account  of  the  heat  taken 
up  by  the  vessel  containing  the  water. 

Suppose  the  vessel  to  he  copper,  vi'  i.iass  ///, ,  and  to 
become  uniforndy  heated  with  the  watc)-. 

Then  as  before  the  heat  lost  by  the  copper  mass  ?//  is 
c„i{t  —  t,),  that  gained  by  the  water  would  be  M(f,  —  /J, 
that  gained  by  the  calorimeter  would  be  <v//,(/,  —  /,),  since  the 
specific  heat  of  the  calorimeter  i.■^  the  same  as  that  of  the  heated 
mass  M.      Hence 


cm{t  -  t,) 
Therefore  c 


M(t^-t,)^ 
,n(t-fS-9n\{f^-t,y 


(2) 


a  formula  from  which  r  can  be  calculated  if  observations  be 
made  for  the  other  terms. 

Having  determined  the  specific  heat  of  copper,  the  calo- 


HEAT. 


119 


or 


(3) 


rimoter  can  now  be  usinl  to  determine  the  si^citie  heat  oi  any 

other  ttubstanue. 

Thus  if  5  be  the  Kixscitic  lieut  of  wyx^r,  c,  thut  of  nnothcr 
BubBtance  of  maw  ///  tu  be  detenniiied,  all  the  other  condi- 
tiona  remaining  tiie  sauu*, 

'"{t-Q     '  •   •   • 

in  which  c  iB  known. 

The   value  etn,  is  culled  the  "water  e<iuivalent "  of  the 

calorimeter. 

Practical  Directions.— Weigh  carefully  m,  the  mass  of 
copper  the  B]>ecifie  heat  of  which  is  to  be  determined. 

A  suitable  mass  of  copi)er  can  be  made  by  twisting  bare 
copper  wire  around  a  lead-i)r-icil,  making  a  mass  about  two 
inches  in  length  and  one  inch  in  diameter.  The  hole  in  the 
centre  will  be  a  suitable  place  in  which  to  insert  the  ther- 
mometer. 

Through  a  cork  in  the  top  suspend,  by  a  thread,  this  mass 

inside  the  cylindrical  heater. 

Adjust  the  length  of  the  thread  till  the  mass  is  about  half- 
way down  the  heater. 

Let  a  thermometer,  through  the  cork,  down  into  the  centre 

of  the  mass. 

Turn  on  the  steam  from  the  hypsometer,  and  let  it  flow 
steadily  for  about  half  an  hoiir,  or  until  the  thermometer  sliows 
a  steady  temperature  between  95°  and  100°.  A  temperature 
of  about  98°  can  usually  be  obtained. 

While  the  steam  is  flowing,  weigh  carefully  the  calorimeter, 
which  should  be  of  copper,  and  stirrer,  m,. 

Partially  fill  the  calorimete.  xith  water  and  weigh  again,  W. 


'- 


;  111 


H 


120 


Laboratory  physIvs. 


I   i 


Fix  the  caloriir-o  r  to  the  attachments  provided  for  tli6 
purpoisc  in  tlie  Ix  .\,  luiJ  svx  ti:<.;  second  tljennometer  into  it  bj 
means  of  the  clij   .ir  aciuiicnt. 

Just  hefure  t'-opuiui;  tlie  liot  nia^s  of  coi)per  into  the 
calorimeter,  stir  tlie  water  in  the  calorimeter  and  read  the 
thermometer,  t^. 

liead  tlie  thermometer  in  the  heater,  t. 

Kow  slide  the  calorimeter  under  the  slot  in  the  heater, 
and  quickly  lower  the  mass  of  copper  into  it. 

As  soon  as  the  co})per  is  under  the  water,  cover  the  calo- 
rimeter and  stir,  watching  the  tiiermometer  and  reading  it 
when  it  reaches  the  highest  poi'  t,  f^. 

A  suitable  cover  for  the  calorimeter  can  be  easily  made 
from  a  i)iece  of  felt  with  holes  in  it  for  stirrer  and  thermom- 
eter. 

Substitute  these  values  in  formula  (2)  and  calculate  c. 

Determine,  with  the  same  calorimeter,  the  specific  heat  of 
zinc,  using  formula  (3). 

Example. — Enter  residts  thus: 


Copper. 

111 

VI, 

w 

M 

(IK-  III,) 

t 

'. 

20.7 

c 

95.3 

45.2 

175.5 

ISO.  3 

98.5 

15.5 

.094 

Blanl-  to  he  filled  in  hy  student. 
Copper. 


Ill 

'"l       1      "' 

M 

t 

u 

t, 

c 

1 

HEAT. 


1-21 


Zinc. 


75.5 


45.2 


4.2 


180.7 


135.5 


lilank  to  he jilled  in  hij  fttiiJent. 


Zinc. 


m 

'"i 

cm, 

W 

M 

t            u 

u 

c 

39.  TO  DETERMINE  THE  LATENT  HEAT  OF  FUSION 

OF   ICE. 


W 


References. — Preston,  pp.  2>So-2S5;  IJarker,  p.  306; 
Carliart,  pt.  ii.  61;  Watson,  p.  246;  Knott,  p.  222; 
Xichols  and  Fi  an,  vol.  i.  p.  171  ;  Ames,  p.  229;  Hast- 
ings and  Beach,  p.  191 ;  Anthony  and  Brackett,  p.  214. 

Apparatus  Required. — A  calorimeter  and  stirrer,  similar 
to  that  used  in  "Method  of  Mixtures"';  a  pair  of  crucible- 
tongs  ;  a  thermometer. 

Theory  of  Experiment. — During  fusion  heat  is  absorbed 
by  a  substance  without  changing  its  temperature,  and  an 
equal  quantity  of  heat  is  disengaged  again  during  solidifica- 
tion. The  latent  lieat  of  fusion  of  a  substance  is  the  heat 
required  to  convert  one  gram  of  the  substance  from  a 
solid  to  a  liquid  state  without  changing  its  temjierature. 

Suppose  a  quantity  of  ice  of  weight  W  to  be  droj)ped  into 


\  \ 


w 


I  '< 


122 


LADOltATOHY  PHTSICS. 


a  quantity  of  water  of  weiglit  jr,  and  temperature  ^, ,  and  the 
whole  stirred  until  the  ice  is  melted  and  the  water  is  of  uni- 
form temperature  t. 

The  heat  absorhed  hy  the  ice  without  clianging  its  tem- 
perature is  LW\  where  L  is  the  latent  heat  of  fusion  of 
ice. 

The  weight  W  has  furthermore  been  raised  to  n  temper- 
ature t,  80  that  the  total  heat  taken  up  by  the  ice  in  melting 
and  raising  it  from  0^  C.  to  t  is 

LW-\-  Wt. 

The  heat  lost  by  the  water  is 

Wit,  -  t). 
Hence  L  W+  Wt  =  {t,  -  t)  ir, , 


and  tlierefore 


_  W^{t.  -f) 


(1) 


In  this  case  we  have  neglected  the  loss  of  heat  of  the 
calorimeter. 

Denoting  by  C  the  specific  heat  of  the  calorimeter,  and 
its  weight  by  ir, ,  C  If,  is  its  water  equivalent,  so  that  the 
heat  loss  is  really 


Hence  LW -^  Wt  =  {  IF.  +  C  1V,){t,  -  t), 


and  therefore 


^  —  1^  fj'      '      (2) 


.,,^:.^-^^^;g^^»'v^g^^^ 


HEAT. 


123 


from  which,  if  the  necessary  observations  be  niade,  L  can  be 
calenlated. 

Practical  Directions. — Weigli  carefully  tlic  calorimeter 
and  stirrer,   11.,. 

Partially  till  the  calorimeter  with  water  warmed  until  it  is 
aboiit  7°  or  8°  above  the  temperature  of  the  room. 

Weigh  again,  denoting  the  weight  by  m. 

Then,   Jl',,  the  weight  of  water,  is  ecj^ual  to  in  —   W^. 

Wrap  a  piece  of  ice  in  a  dry  cloth  and  break  it  into  small 
pieces  with  a  mallet. 

Wrap  pieces  of  cloth  around  the  points  of  the  crucible- 
tongs,  and  pack  ice  around  them  to  cool  them  to  0°  C 

Stir  the  water  in  the  calorimeter  and  read  carefully  the 
tenjperature  ^,  before  dropping  in  the  ice. 

Drop  in  small  pieces  of  ice  with  the  tongs  (carefully 
drying  each  piece  on  the  cloth  before  so  doing),  and  stir  the 
calorimeter  steadily. 

Continue  the  process  until,  all  the  ice  in  the  calorimeter 
being  m^^lted,  the  temperature  of  the  '>vater  is  as  nmch  belo»v 
the  temperature  of  the  room  as  it  was  above  before  beginning 
to  put  in  the  ice. 

Read  the  temperature  ^,. 

Weigh    again  the  calorimeter,    denoting  the  weight   by 


in. 


Then  ir,  the  weight  of  ice  added,  is  equal  to  m^  —  m. 
C,  the  specitic  heat  of  the  substance  of  which  the  calo- 
rimeter is  made,  is  supposed  known,  and  hence  C'lV^  is  known. 
Calculate  Z  from  formula  (2). 


I 


I  i 


£ 


124  LABORATORY  PHTSICS. 

Example  — Enter  results  tlius : 


^y* 

C 
.095 

m 

'. 

t 

m, 

W 

(m,  -  m) 

L 

45.2 

95.7 

50.5 

20.2 

1 

12       100.6 

4.9 

79.6 

Blank  to  be  Ji lied  in  hi/  student. 


"', 

c 

m 

<i 

( 

m, 

IT 

(m,  -  m) 

L 

40.  TO  DETERMINE  THE  LATENT  HEAT  OF  STEAM. 

References — Preston,  p.  304;  Nichols  and  Franklin, 
vol.  I.  p.  171;  Anthony  and  Brackett,  p.  22S;  Hastings 
and  Beach,  p.  191;  Ames,  p.  287;  Carliart,  pt.  ii.  p.  74; 
Watson,  p.  248 ;  Barker,  p.  325 ;  Knott,  p.  224. 

Apparatus  Required. — A  snitahle  calorimeter;  a  boiler 
with  suitable  drying  apparatus  attachment ;  a  thermometer. 

Theory  of  Experiment — By  the  latent  heat  of  steam  is 
meant  the  heat  required  to  convert  a  gram  of  water  at  100° 
C.  into  steam  without  altering  its  temperature. 

Suppose  J/,  a  mass  of  water  in  a  calorimeter,  the  mass  and 
specific  heat  of  the  calorimeter  being  ni,  and  c  respectively, 
to  be  at  a  uniform  temperature  /,  and  that  there  is  passed  into 
it  a  mass  of  dry  steam  w,  at  a  temperature  t, ,  which  on 
entering  the  water  is  conden.sed,  the  whole  being  brought 
to   a    uniform   temperature   /, ;    then,    denoting    the   latent 


y^jf^T?>^^'*mmy^ ' 


HEAT. 


125 


heat  of  steam  by  Z,  the  amount  of  heat  given  out  by  the 
steam  is 

and  the  heat  gained  by  the  water  and  calorimeter  is 

(M  +  an,){f,  -  t). 
Hence         Lm,  +  m,{t,  -  /,)  =  {M  +  cm .)(^  -  0, 


or 


•  • 


(1) 


i,  can  be  calculated  from(l)  if  the  necessary  observations 

be  made. 

Practical  Directions.— Weigh  carefully  the  stirrer  and  calo- 

rimeter  m,. 

Partially  till  the  calorimeter  with  water  and  weigh  again, 

denoting  the  weiglit  by  W.     Then 

The  temperature  of  the  water  should  be  reduced  as  neurly 
to  0°  C.  as  possible,  and  when  heated  by  the  steam  should  be 
raised  as  much  above  the  temperature  of  the  room  as  it  was 
previously  below  it. 

If  tlie  temperature  of  the  water  be  6°  C,  the  room  beinjr 
at  17°  C,  the  water  can  'oe  raised  to  29°,  giving  a  rise  of  24". 

The  water  should  be  stirred  just  before  the  steam  is 
allowed  to  How  into  it,  and  the  temperature  i  read. 

A  special  arrangement  for  a  boiler  or  hypsometer  is 
necessary  to  <lry  the  steam,  and  prevent  it  condensing  atid 
thus  losing  its  latent  heat  before  it  reaches  the  water  of  the 
calorimeter. 

A  suitable  arrangement  is  to  let  the  outflow  of  steam  be 
from  a  spiral  tube  inside  the  steam-chamber  of  the  hypsom- 
eter  or    boiler,  the  spiral  liciiig  so  a<l justed  that  while  the 


-.^y^y-'< .  '^-^?y^^--;^ 


12(5 


LMiOIiA  TOR Y  PHYSICS. 


stean.  flous  throuirl,  it,  it  is  also  surroun.led  hy  ti.e  Bteam 
the  result  bein^^  that  llie  stea.ii  which  passes  into  the  water 
becomes  thoroughly  dried. 

A  short  -lece  of  rubber  tubii.g  makes  a  suitable  comiection 
on  the  outside. 

The  rul)ber  tubing  should  be,  liowever,  carefully  jacketed 
with  cotton  woo!  or  felt,  so  as  to  prevent  condensation  of  the 
steam  before  reaching  the  wutei-. 

Let  the  steam  How  freely  for  a  couple  of  minutes  to  permit 
the  connection  to  get  thoroughly  hot  and  dry 

Pinch  the  end  of  the  rubber  tubiug  and  insert  in  into  the 
caloruneter. 

Let  the  steam  riow  for  a  few  minutes,  stirring  tl)e  water 
all  the  tune. 

AVhen  the  required  ten.perature  is  approached,  pinch  the 
tube  agam  and  .p.ickly  remove  it  from  the  water. 

Stir  the  water  and  read  the  thermometer,  /„  at  its  highest 
pomt.  " 

J!»I"ow  weigh  the  calorimeter  again,  IF';. 

Read  the  barometer  B  and  obtain  t,  from  the  temperature 
curve  for  steam. 

Substitute  in  the  formula  and  calculate  L. 
Example.— Enter  results  thus: 


161.11 


If 


M 


a36.61il75.50 


5.9     75.18 


'. 

', 

99.7 

29.0 

:^43.86;  7.25  '  535.5; 


^f'lnk  to  he  fill,,}  h,  hy  alnd'nt. 


M 


B 


U         «r, 

m. 

/, 

^:^jvv  ^f^- 


■*.:'^ 


'r^r 


MACJNETISM. 


41. 


TO  OBTAIN  A  REPRESENTATION  OF  LINES  OF 
FORCE  WITH  IRON  FILINGS,  AND  TO  BLUE-PRINT 
THEM. 


References.— Watson,  pp.  589-007;  Hastings  and  Bcacli, 
p.  355;  S.  Thompson,  pp.  105-113;  Ames,  p.  347;  Car- 
hart,  pt.  II.  p.  310  ;  Anthony  and  Bruckett,  j).  259  ; 
Nichols  and  Franklin,  vol.  11.  p.  27;    Barker,  p.  633. 

Apparatus  Required. — A  selection  of  permanent  majrnets ; 
irontiluigs;  a  sprinkler  for  tilings;  glass  plates;  blue-print 
paper;  some  disks  of  soft  iron. 

Theory  of  Experiment. — Iron  being  a  paramagnetic  metal, 
if  free  to  move  in  the  vicinity  of  a  magnetic  field,  will  tend 
to  set  itself  in  the  strongest  part  of  the  field.  If,  therefore,  a 
glass  plate  be  laid  over  a  bar  magnet  and  iron  filings  be 
sprinkled  nniforndy  over  it,  the  filings  Mill  set  themselves 
along  the  lines  of  force  when  the  plate  is  vibrated.  After 
the  vibration  the  filings  will  be  very  dense  ju.-t  around  the 
poles,  where  the  field  is  strongest,  and  will  be  thinnest  near 
the  corners  and  sides  of  the  plate,  where  the  field  is  weakest. 

Practical  Directions Select  a  glass  plate  at  least  4  inches 

longer  than  the  magnet  and  about  S  inches  wide.  Place  the; 
iiui'Miet  to  be  investi>;atcd  ceiitrallv  ntider  the  plate  and 
sprinkle  the  iron  filings  in  a  thin  even  coating  all  over  the 
plate. 

in 


128 


LADOHATOHY  PHYSICS 


!*»»  ;■.  i 


Hold  down  tlie  plate  witii  one  hand,  and  vibrate  it  gently 
by  shai-j)  taps  of  the  lingers  of  the  other. 

Lay  the  plate  on  a  piece  of  blue-print  paper  in  the  sun, 
and  after  exposing  for  five  or  ten  niiinites,  depending  on  the 
sensitiveness  of  the  paper,  wash  in  water. 
The  following  curves  should  be  obtained  : 

(1)  From  a  simple  bar  magnet. 

(2)  From  a  horseshoe  magnet. 

(3)  From  two  bar  magnets  with  like  poles  together. 
(■A)  From  two  bar  magnets  with  uidike  p<.les  together. 
(5)  From  a  bar  magnet  with  a  disk  of  soft  iron  in  its  field. 
(♦!)  From  a  horseshoe  magnet  with    the  keeper  an  inch 

from  the  poles. 

(7)  From  the  end  of  a  bar  magnet. 
To  be  Noted  and  Explained  in : 

(1)  Tiie  uniform  distribution  of  the  lines  and  concentra- 
tion of  the  tilings  around  the  poles. 

(2)  The  concentration  and  straightness  of  the  lines  between 
the  poles,  atid  the  curvature  and  thinness  of  the  lines  further 
away. 

(.'{)  The  position  of  the  two  neutral  i>oints  and  the  weak 
nature  of  the  field. 

(4)  The  position  of  the  neutral  jjoint,  and  the  concentrated 
field  between  the  poles. 

(5)  The  crowding  of  the  lines  into  the  soft-iron  end  of 
the  field. 

(«)  The  same  as  in  (.>),  and  the  absence  of  lines  elsewhere. 
(7)  The  radial  nature  of  the  field  around  the  jwle. 


s  \ 


''nc^.^^:'^\^&¥',T?^i.C.:; ' 


MAdM-niSM. 


i*jy 


42.  TO  MAP  THE  MAGNETIC  FIELD  ABOUT  A  MAGNET, 
AND  TO  DETERMINE  THE  MOMENT  OF  THE  MAG- 
NET BY  FINDING  THE  NEUTRAL  POINT  IN  ITS 
FIELD. 


REFERENCES.— AirR's,  p.  ?.:>\\  Curlmrt,  p.  3ir,;  S. 
Tliuiiii»>(iii,  p.  li'+:  Wiitson,  |>.  oits;  r,iirkt'r,  p.  031; 
Niclx.Is  and  Franklin,  pp.  L'l  -:.'."i;  Antlionv  and  IJrackett, 
pp.  -J.-i'.t-L'f.^  ;    Ilastiiiiis  and  IJeacli,  p.  .'}»;i. 

Apparatus  Required — \  liar  ina^rnct;  a  small  t'oinpass- 
box;  a  drawinj^-board  ;  a  lar<;e  slieot  of  paper;  a  st't-s(piare ; 
a  pair  of  dividers;   a  centiiiK'ti'r  scale. 

Theory  of  Experiment.— If  a  compass-needle  be  brought 
near  to  a  magnet,  it  will  be  found  to  take  up  a  lixed  direc- 
tion under  tlie  action  of  the  magnet  and  the  earth's  field. 
This  direction  is  approximately  the  direction  of  the  line  of 
uiaguetic  force  passing  through  the  centre  of  the  comjwss. 

Suppose  A  and  //  to  be  the  positions  of  the  ends  of  the 
compass-needle. 

If  now  the  compass  be  moved  so  that  tlie  point  previously 
at  A  is  at  B,  the  new  direction  of  the  line  of  force  can  be 
marked  by  marking  the  new  position 
(7  of  the  point  previously  at  />. 

The  j)roces8  being  continued,  the 
direction  of  the  line  can  be  followed 
until  it  goes  either  otT  the  paper  or 
hack  to  the  magnet  at  another  point. 
Bv  repeating  the  process  a  map  of  the  magnetic  field  can  be 
made. 

In  mapping  the  magnetic  lleld,  a  j)oint  will  be  found 
where  the  action  of  the  earth  is  exactly  balanced  by  the 
action  of  the  magnet.     At  this  point,  tlie  neutral  point,  the 


Is 

Sl| 

/■■ 

/A 

\ 

/„ 

s 

•  R 

-B''^ 

Fi 


••^iAfc^ySiik^ 


sMr'ji^mi6MAmMj»sj^^  K:m 


.  -ti 


130 


LAUOllATOnY  rilYSlCS. 


iictnlle  of  the  compass  not  beiiij,'  uikKt  tlie  control  of  any 
directive  force,  will  take  any  jwhitioii  iiKlitli'ivntly.  No  line 
of  force  will  therefore  pass  throiii,'h  this  i)oint. 

(1)  appose  the  mairnct  be  placed  in  tlic  nia-,Mictic  nierid- 
iun  with  its  .V  pole  pointin-r  north,  then  the  ncntral  point, 
if  the  niairnct  he  a  simple  one,  that  is,  having'  only  two  poles, 
will  lie  on  the  perpendicular  to  the  magnet  at  its  middle 
point. 


Fio  27. 

Let   NS  denote  the   magnet,    in    the    meridian,    K  the 
neutral  point,  ^> A' being  perpen<licular  to  NS^ 

Then  the  force  acting  on  the  needle  at  A",  due  to  ///  the 

7// 

strength  of  each  pole,  is  ^,  /•  being  the  distance  of  the  pole 

from  the  needle.    The  direction  is  shown  by  arrows  (Fig.  27). 
Resolving  these  forces  along  the  meridian,  we  have 

2  m 

][  z=-j  cos  e, 

since  the  earth's  horizontal  component,  //,  is  exactly  balanced 
by  the  magnet. 


Now 


cos  B  = 


where  I  is  half  the  length  of  the  magnet. 


T^^aroFy^pm 


\;^i:tmuiM 


Ilt'UCO 


// 


M.UiyKTISM. 
2m  f      Af 


131 


or 


M=  ///■', 


(1) 


whore  .1/  i>  the  iiioiiioiit  of  the  mairiict. 

[2)  SuppUBt!  tliu  iiiagnct  tu  lie  plaecil  with  its  ^'^  pole  poiiit- 
iii-r  iioi'tii. 

Then  it  is  ovitlciit  that  siiifo  the  action  ot"  the  inai^iut  oii 
a  iiec'tllu  north  of  S  is  tu  turn  ^ 

the  north  pole  towani  .S',  while     (ZZZTZZ^ /i/->N 

the  earth's  lield  tends  to  turn  f 

it     in     exactly     the     oppor-ite  l'""-.  -S. 

iliri'ctio!!,  a  neutral  point  lies  (jii'cctlv  noiih  of  >'. 

Suppose  it  at  a  distance  /•  from  tin-  ciiitrc  ot    the  maiiiict. 

The  attraction  of  a  on  the  needle  at   A    i>  ,   ,   while  the 

(/'  —  /)• 

f       •      1  .       ,.        .       .  '/' 

reinilsion  of  7i  m  tlie  ui)i»o>ite  direction  is         ,    ,  _ 

'■  (''  +  h 

Hence  the  total  force  {»n  the  needle  due  to  the  magnet  is 


1))  ID 


or 


■ih'»i 


wlucli  is  equal  to 

where  31  is  the  moment  of  the  mai^net. 

23fr 
Hence  Jf  =  -r-r^ ^^r,,  since  tlie  needle  is  in  cfpnlihrium 


or 


M 


(•^) 


■PTjaiia»a»rjr3tg«rgsai6armiei»^ii«^/semawBai5»^^  ijWLyvi'rjoiipm^tmf  vs^-hf- 


iS&^:.m^^is:k}^yjssk,^i^%jd^ 


'i'^yi9.- 


/.-^  «'.»■;. 


t 


I  I 


,     1 


■1} 


III 


] 


182 


LA  nouA  TO  It  r  I'll  rsics. 


(3)  Supiwse  tilt)  inajriiet  to  take  up  a  position  other  than 
the  1.  eridiim,  us  A /{  (Fij;.  21»), 
I  et  A'  l)e  the  iieutml  point. 
Then,  resolving  aloii^'  the  meridian,  wo  have 


in 


m 


//  ~  -,  COS  ^,  ±  ^  COS  e, 

^  an<l  ^,  beins;  the  angles 
which  the  lines  drawn  from  the 
poles  to  the  needle  make  with 
the  meridian.  The  sijjn  between 
the  two  terms  is  —  if  either  ^  or 
6^  be  greater  than  90°. 
1 lenco 


(  cos  6',  COS  ^ 

2///  =  3/|^,'± 


)S  ^1 


Fig.  30. 


3/  = 


2 ////•'/• 


/•*  COS  ^,   ±  /•,'  COS  ff 


Practical  Directions.— (1)  Fasten  a  large  sheet  of  paper 
on  a  tlnuviiig-board. 

Liiy  <lown  on  this,  by  means  of  a  magnetic  needle,  the 
direction  of  the  magnetic  meridian. 

Place  the  magnet  with  its  edge  along  this  line,  its  N  pole 

pointing  north. 

Erect  a  perpendicular  to  the  magnet  from  its  middle  point 
and  move  the  compa.ss-box  along  this  line  until  the  needle  is 
at  the  neutral  point.  When  the  centre  of  the  needle  is  at 
this  point  the  needle  will  lie  in  any  direction  indiflereiitly, 
assuming  of  course  that  the  neeillc  is  a  very  short  one  coin- 
partMl  with  its  distance  <"rom  the  magnet. 

To  make  sure  that  the  neutral  point  has  been  found, 
cause  tiie  ncedie  to  spin  round  by  means  of  another  magnet 


III 


MAdSETIS^f. 


V.V.\ 


or  piece  of  iron,  and  n<.tc  the  ^lirtrti-m  of  the  needle  ..n  .•on.- 
ing  to  rest.  When  tbe  nue.lle  ceaneH  to  ti.ke  up  u  lixc-.l  i-om- 
tion  t)ie  re<|uire(l  point  luw  been  found. 

Mark  die  iH»ition  of  the  con.pa.ss,  iind  tin-l  it.s  euntre. 
Meuisure  the  distance  /•.  ,     ,         i 

Take  for  the  ciuivulent  length  of  the  n.agnet  %  the  lengiU 

of  the  har. 

Find  the  value  of  11  from  the  chart  of  the  rootu. 

Substitute  this  value  in  f».rm»ila  tl)  an.l  caUidaf.-  JA. 

i^l)  Now  place  the  inagnet  with  its  -V  pole  puintn.-  north, 
and  move  the  compass  along  the  meridian  until  the  pos.tu.n 
of  the  neutral  point  is  again  found. 

Measure  /•  as  before,  an.l  calculate  J/,  formula  CJ). 

(;?)  IMace  the  magnet  in  some  other  position,  correspi^nd- 
ing  to  m  in  Fig.  2!>.  I'h't  care- 
fully the  magnetic  field  around  the 
niairnet.  It  will  be  fi>und  that 
near  one  point  the  lines  of  fonre 
bead  away,  as  in  Kig.  :5<).  The 
neutral  point  lies  within  this  space 
between  the  curves. 

Adjust  the  position  of  the 
neetUe  as  before  till  no  directive 
force  acts  on  it. 

Measure  /'  and  /*,. 

Drop   perpendiculars,  as   LQ  and    sx  (Fig.    29).  on  the 
direction  of  the  meridian  line  through  1\. 


vn\^ 


V. 


/ 
/ 

/  /■ 
//  /  y 
//  /  '■ 


///  / 


Fio.  30. 


w 


cos  d,  =  jj^\     tios  fy  =  -  ^_- 


Measure  the  distances  corresponding  to  /\'(^>,  LA",  Kx. 
Substitute  in  formula  (:'.)  and  calculate  M. 
Show  diairrani  in  each  case. 


I 


!^( 


111 


134  LABORATORY  PUYSICA 

Example. — Enter  results  thus: 

II  =  .1584. 


1  >,t  case 
2(1  case 
3d  case 

r 

'i 

/ 

AV 

Kx 

LK 

J/ 

24.  T) 
32.0 
80.2 

2JS)() 
23  It) 
2270 

"22.6' 

7.5 

3.95 

3.29 

8.33 

Afp.iTi   vnliir 

of  M     

2291 

Blank  to  he  Jilled  in  l»j  student. 
11  = 


r 

»i 

I 

A'(? 

A'x 

LK 

M 

1st  case 
2d  case 
3il  case 

of   ^                         

* 


43.  TO  DETERMINE  THE  MOMENT  OF  A  MAGNET  BY 
OSCILLATION  IN  A  UNIFORM  FIELD  OF  KNOWN 
INTENSITY. 

References.— S.  Tliomp^on,  p.  1'21;  AVatsoii,  p.  r.04: 
Ames,  p.  352  V  Xiehols  and  Fmiikliii,  vol.  11.  p.  '24:  Aii- 
tliony  and  Uraekett,  p.  SOS;  Carliart.  pt.  11.  p.  .".!!»;  ll.i.^t- 
iii<,'s  and  T?oach,  p.  364;  Barker,  p.  691. 

Apparatus  Required. — An  o.^eillation-ltox  wifli  siisi)ensi(.n  : 
several  macrnets  of  diflFerent  sizes  atid  eorre.^pondinj;  t<.rsi(iii 
weiirlits:   a  niieronieter-iraiiire  :   a  stop-wateli ;   a  e()ni])ass. 

Theory  of  Experiment. — If  a  lllil^n(•l,  of  moiiiuiit  J/,  i»e 


MAGSETI8M. 


135 


allowed  to  oscillate  in  a  unifonn  magnetic  field  //,  the  law  uf 
its  vibration  is  expressed  by  the  forniula 

where  n  is  the  number  of  transits  per  second,  and  K  the 
m(»ment  of  inertia  of  the  nm-net.  If  observation  be  made 
for  A' and  «,  //being  known,  3/ can  be  calculated. 

Practical  Directions.— Lay  down  a  meridian  line  with  the 

compass. 

If  the  bottom  of  the  oseiHatit.n-box  be  provided  with  a 
mirror  which  has  a  line  ruled  centrally  on  it  and  parallel  to 
the  sides  of  the  box,  it  will  be  suthcicnt  to  set  one  side  of  the 
box  along  the  meridian  line.  The  line  on  the  mirror  is  to 
serve  as  the  middle  point  of  the  swing  of  the  magnet. 

Attach  the  torsion  weight,  and  after  it  has  come  to  rest 
turn  the  suspension-head  imtil  the  weight  lies  along  the  line 
on  the  mirror.  Replace  the  weight  by  the  magnet,  bemg 
careful  to  have  the  N  pole  pointing  north. 

Set  the  magnet  swinging  through  15°  or  20  . 

Observe  the  time,  t,  of  fifty  transits  past  the  median  line, 

50 

l^Feasure  the  length,  I,  and  horizontal  thickness,  J,  of  the 
..lagnet  to  -^^  of  a  millimeter. 

Weigh  the  magnet  to  a  centigram. 

Calculate  the  moment  of  inertia  from  formula 


II 
1 1 


A^=ir(-^), 


r  \ 


where  TF  is  the  wt-ight  *d'  the  Uiagnet. 


;^ 


'  !■ 


136 


LABORATORY  PHYSICS. 


Assume  the  value  of  7/  and  calculate  the  moment  of  the 
magnet  from  formula 

^[ake  observations  for  several  magnets  of  different  dimen- 
sions, 

Ezample. — Enter  results  thus : 

11=  .1489. 


No.  of 

5 

I 

weight, 

K 

Time  of 

Trans,  per 

M 

MtiKiiet. 

Onis. 
53  31 

50  Transits. 

Sfcoiiil  (n). 

17 

8.8 

1.3 

350 

420" 

0.1189 

327.8 

18 

8.8 

\:l 

53.81 

354 

440" 

0.1136 

302.8 

1!) 

10.4 

1.0 

25.18 

239 

332" 

0.1506 

341.3 

20 

14.8 

2.0 

154.77 

2877 

500" 

0.1000 

190.7 

Blank  to  he  JiUed  in  hij  shuleni. 
11  = 


No.  of 
Magnet. 

b 

I 

Weight, 

K 

Time  of 
5U  Transits. 

Trans,  per 
Second  (n). 

M 

44-   TO  COMPARE  THE  MOMENTS  OF  TWO    MAGNETS 

BY  OSCILLATION. 

References. — As  in  previous  oxperimont. 

Apparatus  Required. — Two  bai-  magnets;  a  stirru])  bored 
to  lit  tlie  magnets  and  provided  witli  clamj^s  for  fi.xing  tliom 
rigidly  together;  a  bell-jar  or  box  with  su6})onsion ;  a  torsion- 
weight;  a  stop-watch;  a  compass. 


MAGNETISM. 


137 


Theory  of  Experiment. — If  two  magnets,  wliich  are  rigidly 
connected  together,  so  tluit  tliey  niiiy  be  suspended  pandiel 
and  in  the  same  vertical  plane,  be  vibrated  under  the  control 
of  a  constant  magnetic  force,  the  ratio  of  their  moments  can 
be  readily  obtained.  For,  if  they  be  vibrated  (1)  with  their 
like  poles  together,  (2)  with  their  like  poles  opposite,  and  the 
nuinl)er  of  transits  per  second,  /«,  and  //,  respectively,  be 
noted,  we  have 

J/,  =  vi,-^  m,, (1) 


M\  =  m,  —  III, , 


(-0 


where  ill/,  and  M,  are  the  resj)ective  moments  of  the  systems 
in  the  two  cases,  and  m^  and  ///,  the  moments  of  the  separate 
magnets.     We  also  have 


(3) 


//being  the  constant  controlling  force,  which  is  in  this  case 
the  earth's  horizontal  component. 
By  combining  the  above  we  have 


+  < 


«.'  —  V 


(5) 


This  gives  a  very  convenient  method  of  comparison,  and 
is  practically  independent  of  the  size  or  shape  of  the  magnets. 

Practical  Directions. — Having  laid  down  a  meridian  line, 
hook  in  the  torsion  weii;ht  and  lot  it  come  to  rest. 

Turn  the  suspension-head  around  so  that  when  the  mag- 
nets are  susj)endcd  they  will  lie  along  the  meridian. 

Clamp  the  magnets  in  the  stirrup  so  that  they  are  sus- 
pended near  the  middle  of  their  lengths  and  with  their  like 
poles  in  tlie  same  direction. 


.'n.i«B.>  *H  MMtK^amyi^^m  «r  j^-vMsm  ^ 


^mM\.>^m^ 


138 


LABORATORY  PHYSICS. 


Lift  off  the  torsion-weight  and  hook  on  the  magnets, 
being  careful  not  to  have  the  su^^pension  fly  around  in  doing 
so,  a"'nd  that  the  N  poles  of  the  magnets  are  towards  the 

north. 

Let  the  system  come  to  rest,  and  mark  the  point  in  the 

bell-jar  at  each  end  of  the  magnets. 

Set  them  swinging  l)y  means  of  another  magnet. 
Note  the  time  of  titty  transits  past  the  marked  point. 
Koverse  the   lower  magnet,  being  careful  to  clamp  it  in 

the  middle  as  before. 

Observe  again   the  time  of  fifty  transits  jwst  the  same 

point. 

Obtain  the  nnnd)er  of  transits,  v,  and   n,,  in  each  case, 
and  calculate  the  ratio  ?//,  and  m,  from  formula  (5). 

Example. — Enter  results  tlnis: 


Time  of  50  Transits 
with  Like  Poles  toKi'lliHr. 


455 


Time  of  ."OTninsits 
with  l.ike  I'olfs  opposite. 


1140 


0.1099 


7n,  _  vO.1099)'  4  (0.0438)'  ^  j  g^g 
r«,  ""  (0.1099r  -  (O.U438)» 


0.0438 


I'l 


II 


Blank  to  h'  fVc<l  «'"  ^  student. 


Time  of  r>0  Transits 
witli  Like  I'oles  tuRetlier. 


Time  of  .50  Transits 
witli  Like  Poles  opposite. 


7/1,1 


"i 


ilr 


MAGNETISM. 


139 


45. 


TO  FIND  THE  MOMENT    OF   A   MAGNET  BY  THE 
DEFLECTION    METHOD. 


References Wiitsoi:,   p.  <'.0(i;    Ames,   p.  3r>M;     Nichols 

and  Franklin,  vol.  11.  p.  23;  Anthony  and  Hrackett,  p.  L>r.8; 
S.  Thompson,  ]).  124 ;  Carhart,  pt.  11.  p.  318;  Hastings  and 
Beach,  p.  361  :    Barker,  p.  61>1. 

Apparatus  Required. — A  magnetometer ;  a  magnet  whose 
moment  is  to  be  determined. 

Theory  of  Experiment. — Let  a  magnet  of  length  '21  be 
placed  so  that  the  line  of  its  axis  is  at  right  angles  to  the 
majrnetic  meridian,  and  in  line  with  the  centre  of  a  magnetic 
needle.  Let  the  distance  between  the  centre  of  the  magnet 
and  the  needle  be  denoted  by  <l,  Fig.  31. 

N 


n ^ZZiL 


d 


Fig.  31. 


The  attraction  due  to  the  pole  m  on  a  pole  A' will  be 

'}nm^ 

w-ir 

and  the  repulsion  due  to  s  will  be 

WW, 

{d  +77' 

where  in  is  the  strength  of  the  poles  of  the  magnet,  and  //;, 
that  of  tlie  needle  at  K. 


I 

II 


IRI 


li 

t 

ii 


s. 

i 
% 

m 


140  LABORATORY  PHYSICS. 

The  total  attraction  therefore  will  be 

■i<U/n7n. 


mm. 


mm 

—  r,    ,-^.v.  or 


(</  ^  /)'        (</  -I-  ly  "•  (,/'  _  r)'- 

If  the  needle  be  deflected  through  an  angle  ^,  the  moment 
(»f  the  couple  acting  on  the  needle  will  be 

■id/frwi,  C08  ^ 
{d'-iy       ' 

the  length  of  the  needle  being  considered  negligible. 

Since  tlie  needle  is  in  equilibrium,  this  moment  nmst  be 
equal  to  that  of  the  earth's  magnetic  couple. 


Hence 


4dh)im,  cos  6 

id'  -  iy~ 


=  llm.^  sin  ^, 


•     .     (1) 


//being  the  earth's  horizontal  component. 

Denoting  the  moment  of  the  magnet  by  Jtf^  substituting 
this  for  2mZ,  and  solving,  we  get 


(2) 


By  means  of  this  formula  31  can  be  calculated  if  If  be 
known,  d,  /,  and  B  ol)served. 

Practical  Directions. — A  suitable  magnetometer  for  this 
experiment  may  be  made  by  pivoting  a  light  magnetic  needle, 
])rovided  with  long  pointers,  at  the  zero  of  a  scale  graduated 
toward  both  ends,  and  having  at  fixed  distances  from  the 
scale,  and  j)arallel  to  it,  linear  scales  for  reading  the  deflections. 

Place  the  mag!ietometer  so  that  the  needle,  when  in  the 
magnetic  meridian,  is  at  right  angles  to  the  direction  of  the 
maijiietomoter  Bcale. 


MAGNETISM. 


141 


If  a  compass-box,  for  reading  the  deflections  directly  in 
degrees,  be  used,  the  l»ox  should  be  so  adjusted  that  the  north 
and  south  line  is  at  right  angles  to  the  scale. 

If  a  linear  scale,  as  suggested  above,  be  used  for  reading 
deflections,  the  zeros  of  these  scales  should  be  in  a  line  at 
right  angles  to  the  direction  of  the  magnetometer  scale. 

Place  the  magnet  whose  moment  is  to  be  determined 
so  that  it  lies  along  the  magnetometer  scale,  its  N  yiole  point- 
inc  to  the  needle  and  at  a  distance  from  it  of  from  25  to  50 

cm. 

If  /•  and  y,  denote  respectively  the  distance  of  the  N  and 
S  poles  of  the  magnet  from  the  needle,  then 

r  -\-r^ 

d  =  -- -— . 

Read  the  deflections  on  the  linear  scales. 

Reverse  the  magnet,  the  S  pole  being  now  a  distance  ?• 
from  the  --inodle,  and  again  read  deflections. 

Similarly  i)lace  the  magnet  at  a  distance  row  the  opposite 
side  of  the  'icedle,  reversing  as  before  and  reading  deflections. 

Denote  the  mean  of  the  eight  deflection  readings  by  ^. 

Measure  the  distance  between  the  two  linear  scales,  denot- 
ing this  length  by  2a ;  then 


tan  ft  =  —. 
a 


To  find  the  length  I,  measure  by  means  of  a  centimeter 
scale  the  length  of  the  magnet,  and  take  \  of  this  as  the  true 
length,  or  2Z. 


//  is  given. 


Substitute  these  values  in  the  general  formula  (2^  and 
calculate  M. 


142  LAnoRATonr  /v/iAVt-s. 

Example. — Enter  results  tlius : 


PoHition  of  MsKDet. 

r 
30.0 

r, 

42  6 

d 
38.3 

2.32 
2.34 
2.32 
2.35 

2.35 
2.34 
2.34 
2.35 

a 

Kast  of  nt-etllif 

2.33 
2.34 
2.33 
2.34 

Heverseil 

Wewt  of  nt'etlltf 

30.0 

42.6 

88.3 

Keversed 

Mean  values 

36.3 

2.33 

tf  =  5cui.,       /  =  5.12,       II-.  .150; 


M^ 


.150Jj3«,30)'  -  (5.12)' i'^        2.83 
2  X  36.30  ^      6 


=  1606. 
Blank  to  he  filled  in  hy  stndent. 


Position  of  MaRnet. 

r 

'i 

d 

<. 

«. 

< 

East  of  needle 

Keversed 

West  of  needle 

Reversed 

Mean  values 

a  = 
M  = 

1  = 

= 

E: 

= 

MAUShTISM. 


143 


46.  TO  DETERMINE  THE  MOMENT  OF  A  MAGNET  BY 
MEANS  OF  THE  TORSION  BALANCE. 

References.— S.   Tljompsoii,   j).    IT.*;    IJarker,    \>.    '»■'{!»; 
Antliony  and  Urackett.  y.  1-Jl;  Carliart,  pt.  11.  p.  1»51. 

Apparatus  Required.  — A  ('oulonil)  balaiice  provitled  witli 
a  <?railuated  torsion-lit-atl  and  lower  circle;  half  a  meter  of 
tine  wire  for  the  siii^I>eiisioii;  a  Imiij,'  cylindrical  l.rass  har;  a 
ion"  cylindrical  inair.iet ;  aconnuis;^;  a  watch;  a  micruineter 
gauge;  a  centimeter  scale. 

Theory  of  Experiment.—  If  a  magnet  of  moment  M  be 
8uspended  horizontally,  and  detlccted  through  an  angle  e 
from  the  meridian  of  a  magnetic  field  whoso  horizontal  com- 
ponent is  7/,  by  X  turns  of  a  suspending  vire  having  a  tor- 
sion couple  T  \>er  unit  angle,  the  condition  of  ecpiililmum  is 

27rXT=  Jflf  sin  0 (1) 

If  a  non-magnetic  bar  of  known  moment  of  inertia  be 
oscillated  in  the  stn-rup  carried  by  the  suspeusioi.  wire,  the 
value  of  T  can  be  found,  suice 


T  =  n-'nK, 


(2) 


where  n  represents  transits  per  sec,  and  K  the  moment  of 
inertia.  To  compare  the  moments  of  two  magnets  by  this 
method,  it  is  onlv  necessary  to  observe  the  turns  of  the 
torsion-head  re(iuired  to  deflect  them  through  the  same  angle, 
when  the  moments  will  be  to  each  other  as  the  turns  of  the 

torsi  on -head. 

Practical  Directions.— Weigh  and  measure  the  brass  bar 

to  the  second  decimal  place. 

Set  it  in  the  stirrup  and  level  the  instrument  so  that  the 
bar  may  swhig  freely  all  round. 


[ 


144 


LMiORATOltY  I'llYMirs. 


Set  it  oscillating  tliroiigli  2<>  or  30  ilegrccs,  and  observe 
the  time  of  twenty  transits  jMist  the  niiddle  point  of  its  swing. 
Denoting  the  time  by  <, 


n 


t-'O 


Calculate  A' from  formula 
A 


''='"(l':i+[r.) 


in,  I,  and  e  being  rcspectivi'ly  the  weight,  length,  and  diameter 
of  the  brasH  bar. 

('alculate  7'  from  fonnula  (2). 

Having  bruuglit  the  brass  l>ar  to  rest,  turn  the  torsion- 
head  till  the  brass  bar  lies  i)aral]el  to  the  direction  of  the 
meridian  as  determined  liy  the  compass. 

Note  through  which  diametrically  opposite  graduations 
on  the  lower  circle  the  meridian  passes. 

Kemove  the  bar  and  replace  it  by  the  nuvgnet,  being 
careful  to  have  the  N  pole  pointing  north. 

Twist  the  torsion-head  so  that  the  magnet  is  deflected 
throuirh  an  atigle  of  »".n°  (,i-  7u'  (W). 

licad  the  whole  and  fracti(tnal  turns  of  torsion-head. 

iJring  the  l)ar  back  to  the  meridian  and  diHect  it  through 
the  same  angle,  ^^  on  the  other  side. 

Let  j>  denote  mean  turns  of  torsion-iiead. 

Then  .V  of  fonnula  (1)  is  e(]ual  to  I  J*  —  „,.    I,  since  the 

magnet  is  deflected  through  the  angle  ^. 

The  value  of  //is  snp})osi'd  to  be  known. 

Calculate  the  moment  (»f  the  givou  nuignet  from  the  for- 
mula (1) 


MAOSKIIHM. 


145 


Precaution.— As  tlie  mngjict  nears  the  east  and  west  posi 
tion,  l>u  curtfiil  to  kt-ej)  it  from  swinging  widely.     If  allowed 
t<»  i)a8.s  the  aliovc  position,  it  will  .swing  conii»letely  around. 

Example.— Enter  results  thus: 


BUA88  HOI). 


w 


37  m 


18  14 


.500 


MAGNET. 


//   -  .119. 

* 

Tuniii  (.f  T 
head 

irMion- 

Mean  p. 

1 

--'-;„• 

M 

SO'.O 

Right 
2.48 

Left 
2.46 

!         2.47 

1 

2.35 

941 

Blanks  to  be  Jill ed  in  by  fftiuhnt. 
BRASS  ROD. 


w 

I 

c 

K 

n 

T 

• 

//  = 


MAGNET. 


« 

Tunis  of  Torsiiiii- 
head. 

Mean  p. 

M 

1 
1 

Tap 


UA 


LABORATORY  PHT81C8. 


4/.  TO  DETERMINE  THE  HORIZONTAL  INTENSITY  OF 
THE  EARTH'S  MAGNETIC  FIELD  BY  THE  MAG- 
NETOMETER METHOD. 

References.-  S.  Thuin|)i«)n,  pp.  121  and  124;  WaioDn,  p. 
615;  Ames,  p.  355;  Nicliol«  and  Franklin,  p.  23;  Anthony 
and  Bnickett,  p.  26s. 

Apparatus  Required. — A  permanent  bar  magnet  (prefer- 
ably cylindrical);  a  delicate  mirror  magnetometer  with  wilk- 
tihre  suspension  and  j)rovided  M'ith  a  long  centimeter  scale ;  a 
telesco|)e  f<»r  reading  deflections  of  the  magnetometer- needle. 

Theory  of  Experiment.— Let  the  middle  uf  a  iKrmanent 
ntagnet  of  moment  J/  be  brought  up,  in  the  end-on  luisition, 
to  a  distance  r  from  the  centre  of  a  delicately  suspended 
magnetic  needle.  Let  the  needle  be  deflected  in  conse<iuence 
throngh  an  angle  0.  Then,  if  //,  be  the  value  of  the  con- 
trolling force  on  the  needle  (in  this  case  the  horizontal  in- 
tensity of  the  earth's  field), 

^    /^.(^•'  -  n  tan  H 


J/  = 


(see  page  140),  where  I  is  one-half  the  magnetic  length  of 
the  defiectitig  magnet.  Tf  now  the  deflecting  magnet  1)6  sus- 
pciided  by  a  fine  thread  and  allowed  to  oscillate  freely  under 
the  action  of  the  earth's  field,  then 

Mir,  =  n'n*K, (2) 

where  A'  is  the  moment  of  inertia  of  the  magnet,  and  n  the 
number  of  transits  per  second. 

Solving  between  (1)  and  (2),  we  get  j  r  //, 


jr  _      nn        1 2  Kr 

'  ~  ?  —  /' V   tan  t)' 


(3) 


^iS 


^j^ 


.VAfUf/cris.v. 


147 


TIk!  taiij^'CMit  of  fill'  uiij^lf  of  (li'Hcctiuii  is  ^-.-     wln-rc  />  is 

tlu'  diNtiiiici'  from  suspeiulctl  ihmmIIc  t<»  i1h-  schIu  of  the  tele- 
hi'opi!,  and  'li  till!  mean  «li'tU'(;ti()ii  of  the  iit'i'<lle. 


Hence 


,,  27T»  //A 


If 


.      .     .     (4) 


Practical  Directions. — Lcvti  tin-  ina^'nrtometi'r  -o  that  tin- 
needle  Kwiii^'s  freely.  Set  tlir  i-ale  east  iiin!  \v(->t  I'V  means 
of  tin- elamiw  provided.  Tlu'  (■  x\\\  ol  'u'  >cale  whuuld  !»o 
under  the  needle  approximately. 

Set  up  the  telescope  and  m-;  le  it  a  M-air  distance  />  of 
about  one  meter.  Adjust  the  •eW'scupi-  to  point  on  the 
iiiirn)r,  and  while  lookiiif;  aloii-  the  tflt',-..upc,  adjust  the 
scale  up  or  down  tintil  an  imi!   o  tf  if  is  si^eii. 

Focus  til'  telescope  on  l  i-  image  ''  the  scale  in  the 
mirror. 

Adjust  the  telescope  and  -  '<■  till  tin  zno  readiiij;  is 
opposite  the  vertical  cross. 

Turn  the  scale  of  the  telt-'  -pc  until  its  •  luls  are  equi- 
distant from  tlie  needle. 

Place  the  deflecting  majrii'  its   -tir;  .       'ii   the  scale 

provided  for  it  and  hring  it  up     >  ;»     .>tan<  *■  /     -<     that  a  de- 
flection of  1<M»  mm.  or  so  is  ohtaii    >\ 

liead  the  deflection,  f?,,  to  ,'„  mm 
heinir  careful  to  have  the  centre  of  t' 
distance,  /',  as  hcforc. 

Read  deflection,  <■?,. 

Transfer  the  magnet  to  the  other  m.ii-  of  M.-  iia^itetom- 
eter  at  the  same  di^tance,  r.  and  ohtai  -iii  i  uly  the  read- 
ings. rf„  6^. 


Iv'     •  I-     I    ■■  ii.agiict. 
'n;,^iic!     it    tli<-   -ame 


J 


3  «| 


148 


LABORATORY  PIir.SlCS. 


A  mean  of  the  four  readings  should  be  taken.  Hence 
the  data  for  formula  (1). 

Now  unhook  the  needle  from  tlie  magnetometer  and  re- 
place it  by  the  deflecting  magnet  (a  small  aluniininm  wire 
stirrup  is  convenient  for  Bupporting  the  magnet). 

Set  the  magnet  swinging  and  count  the  time  of  tifty 
transits. 


50 


If  t  be  the  time,  then    )i  =  —. 


Measure  tao  length,  /,  and  diameter,  f,  of  the  magnet 
with  a  pair  of  micronieti     calii)ers. 

Weio-h  the  magnet  to  ^\  milligram,  denoting  the  weight 


by  w 


Calculate  ^from  the  formula  for  cylindrical  bars: 


^='<Fi  +  S) 


Calculate  the  value  of  the  earth's  horizontal  field  from 
formula  (4). 

Example. — Enter  results  thus : 


MAGNETOMETER  OBSERVATIONS. 

1 

Deflections,  mm. 

M«*aii 

r 

«l 

f                  J, 

«4 

146 

146      1      149 

140             145 

GO.  75 

40 

MAONETISM. 
OBSERVATIONS  ON  MAGNET. 


149 


Weight. 

Length. 

Diameter. 

n. 

13.545 

10.2 

0.48 

0.26 

ir  =  13.545  {M-'+^^,^q  =  117.6. 
2  X  3.1416 


fl.  = 


(40)- 


416  X  ^^26  ./ri7.6  X  66.75  X  40  _   1523. 
-  (4.5)'      ^  14.5 


Blanks  to  heJiUcd  in  by  student. 
MAGNETOMETER  OBSERVATIONS. 


Deflections,  mm. 

Meaa 
i 

D 

r 

«. 

il 

<• 

«4 

\ 

OBSERVATIONS  ON  MAGNET. 


Weight. 

Len(;th. 

Diameter. 

n. 

K  = 


.*  "-.■v^rc^.*'j». 


'":i^t:^k^   'kM.p^i'ca^.jUM:^^^:' 


^ 


150 


LABORATORY  PHT8IC8. 


48.  TO  DETERMINE  THE  EQUIVALENT  LENGTH  OF  A 

MAGNET. 

References. — As  in  Experiment  45. 

Apparatus  Required. — A  compass-box;  a  magnetometer 
with  telescope  and  scale  or  lamp  and  scale;  a  permanent 
magnet. 

Theory  of  Experiment. — Suppose  that  a  permanent  mag- 
net, ABy  is  })laced  at  right  angles  to  the  magnetic  meridian 
and  with  its  centre  at  a  perpendicular  distance  r  from  a 
small  magnetic  needle  at  C. 


FiQ.  32. 
The  force  exerted  by  the  N  pole  is 


in 


V  +  .-' 


and  in  the  direction  A(J^  m  being  the  strcngtli  of  the  pole, 
and  I  half  the  length  of  the  magnet. 
The  force  exerted  by  the  S  pole  is 


VI 


r  4-  #•" 


and  in  the  direction  OB. 


MAGNETISM. 


151 


The  resultawt  of  the  two  forces  deflecting  the  needle  is 
evidently  along  the  line  ElV,  and  is  equal  to 


2m      . 
^,-^-.sin0, 

0  being  the  angle  so  marked  in  the  figure 

sin  0  = 


I 


vr  +  / 

Hence  the  resultant  along  EW  is  equal  to 

2ml 

The  moment  of  this  for'^e  on  the  needle  is 

2ml 


,«\l 


(?  -f  r') 


cos  &, 


6  being  the  deflection  of  the  needle. 

This  is  equal  to  the  eartli's  magnetic  couple. 


Hence 


2ml 


or 


2ml 


cos  ^  =  ff  sin  9, 


1=  //tan  e. 


(1) 


Suppose   now  the  magnet   +o  be  brought  to  a  position 
distant  /-,  from  the  needle,  the  new  deflection  being  ^,. 


Then 
Hence 


2ml 


i  =  //  tan  ^,.      .     .     . 

{I'  +  '•.')' 

{K±r"y  ^  tan  d 

(^4  /)»  tan  d,' 


(2) 


■'3Mk^^\'^.mM. 


u^. 


l1 


m 


152 


or 


Denoting 


LAliOUA TOUT  PJnslCS. 
r  +  /•,'     __  /tan  ^  \< 


ii!ul  >olviiig  for  1,  we  get 


'-^'t^:^- 


(3) 


If  ;',  /*,,  d^  ^,,  be  observi'd,  ^  can  l»e  caloulatecl. 

This  position  of  the  magnet  with  relVivnce  to  the  needle 
is  called  the  "  Broadside-on  I'otiition." 

(•2)  Suppose  tlie  magnet  to  l>e  placed  at  right  angles  to  the 
meridian,  and  its  axis  in  a  line  with  the  centre  of  the  needle, 
as  in  Fig,  33. 


r 


Fig.  33. 


The  conditions  now  are  the   same  as  in  obtaining  the 
moment  of  the  magnet  by  deflection  method. 


Hence 


4  rim 


-,  =  IlUxn  H,    .     .     .     .     (4) 


6*,  r,  and  I  having  the  same  meaning  as  before 
For  a  position  distant  /■,  we  also  have 


■i^rj/ii.  ^^ 


(5) 


^ 


MAONETIS^. 


153 


Combining  (4)  and  (5)  and  solving  for  l^  we  get 


A  being  equal  in  this  case  to 

lr^  tan  ff^ 
\r  tan  Bj  ' 

From  (6)  I  can  be  again  calculated  if  ^,  (f^  r,  and  r  be 
observed. 

This  is  known  as  the  ''  End-on  Position." 

Practical  Directions.— (1)  Broadside-on  Position.— ?\Ace 
the  magnetometer  in  the  magnetic  meridian,  and  focus  the 
telescope  on  the  scale,  the  telescope  being  in  a  line  east  or 
west  of  the  magnetometer. 

Place  the  magnet,  whose  magnetic  length  is  to  be  deter- 
mined, at  right  angles  to  the  meridian,  having  its  centre  and 
the  centre  of  the  needle  in  the  meridian. 

Adjust  the  distance  till  a  deflection  of  nearly  the  whole 
scale  is  obtained. 

Now  reverse  the  magnet,  and  read  again.  The  mean  of 
the  observations  gives  the  true  value  for  the  deflection. 

Denote  the  mean  deflect'on  by  6. 

Measure  the  distance  r.  Allowance  should  be  made  for 
the  width  of  the  magnet. 

Adjust  the  position  of  the  magnet  to  another  distance,  /•,, 
so  that  a  deflection  of  about  half  the  previous  one  is  obtained. 

Read  deflections  and  take  the  mean  as  before. 

Measure  r,. 

Measure  the  distance  between  the  magnetometer  and  the 
telescope  scale,  denoting  it  by  K. 

Calculate  (: ^*l'     or     A^ 

Han  bj  * 


% 


154 


LABORATORY  PHYSICS. 


I 


1 


remembering  that  tan  2  #  =  jv,  since  the  reflected  angle  ia  double 

the  deflection  of  the  mirror. 

Substitute  in  formulii  (3),  and  calculate  /. 

(2)  End-on  Position. — Now  place  the  magnet  at  right 
angles  to  the  magnetic  meridian,  its  axis  being  in  a  line  with 
the  centre  of  the  needle. 

Again  adjust  the  tlistance  /•  till  a  deflection  of  nearly  the 
whole  scale  is  obtained. 

Read  ;•  and  the  deflection  as  before. 

Koverse  the  magnet,  and  repeat  the  observations. 

Adjust  again  for  a  deflection  of  about  half  the  previous 
one,  repeating  the  readings  as  above. 

p\  tan  0  \* 


Calculate 


//',  tan  ft  y 
V  Ian  ft  J 


or     A. 


Substitute  in  formula  (6)  and  calculate  /. 
Example. — Enter  results  thus : 


BROADSIDE-ON    POSITION. 


Posiliiiii 
of  Maguet. 

N.  toE. 
N.  to  \V. 
N.  to  E. 
N.  to  W. 

r 

26.3 
33.1 

a            Mean  i 

1 
i 

a: 
42 

A 

1.546 

Calfiilaieil. 

I>>neth 
ot  KHr. 

15.3 

18.9 
18.7 
9.60 
9.30 

18.8 
9  45 

13.8 

E 

ND-OX 

POSITION. 

N.  to  H. 
N.  to  W. 
X.  to  E. 
N.  to  W. 

40 
50 

113 
12.3 
(i.O 
5.65 

11.8 

r».8:J 

41.3 

1.580 

12.7 

15.2 

w  IP  Hi  ■>  im\*        ■ 


.r\wUiA^ 


MAGNETISM. 
Blaiih  to  he  Jill nd  tn  by  Htvdent. 

BROADSIDE  OX    I'OSITIOX. 


155 


] 

Position 
of  MaKiit^l- 

)■ 

i 

Mean  i  \ 

K 

A 

-'          1 
Calculatfd. 

of  Bar. 

1 

:  X.  to  E. 

X  toW. 
X.  to  E. 
X.toW. 

EXD-ox  posniox. 

X.  to  E. 
X.  to  w. 
X.  to  E. 
X.  to  W. 

49.  TO  DETERMINE  THE  VARIATIONS  IN  THE  HORI- 
ZONTAL INTENSITY  OF  THE  EARTH'S  MAG- 
NETIC FIELD  BY  MEANS  OF  THE  COMPASS-BOX 
VARIOMETER. 

References. — Kolilrausch'sPliysical  ^[easureineiits,  p.  257. 

Apparatus  Required. — Kohlrausch's  eoinpass-box  vari- 
ometer. 

Theory  of  Experiment. — The  variometer  consists  essentially 
of  a  permanent  matijnet  and  compass-box,  the  box  being  upon 
the  top  of  an  upri<;ht  which  passes  through  tlie  centre  of  the 
magnet,  the  centre  of  the  magnet  and  the  needle  having  the 
same  vertical  axis.  The  magnet  can  be  adjusted  vertically 
and  turned  round  its  centre. 

Suppose  the  magnet  to  1)e  fixed  with  regard  to  its  vertical 
motion,  and  to  be  turned  n»und  until  its  N  pole  points  north. 
The  corresjM.nding  pole  of  the  needle  in  the  compass-box  will 
point  ilirectly  south. 


i 


15C 


LAjiORAToitr  rinsics. 


1 ' 


If  now  tlie  magnet  he  turned  through  an  angle  6,  such  that 
tli.3  needle  lies  in  an  east  and  west  direction,  we  have 


/''cos  0  =  B^, 


(1) 


wlu-re  J^  is  the  force  due  to  the  magnet,  and  ff,  the  eartli's 
liori/oiital  component. 

Now  let  the  instrument  be  moved  to  another  station, 
where  //,  is  the  earth's  horizontal  component. 

If  now  the  magnet  bo  turned  through  the  same  angle,  6^, 
from  the  meridian,  the  needle  will  take  up  a  different  position. 


Fio.  34. 

making  an  angle  0  with  the  east  and  west  direction  (see  dotted 
line  in  Fig.  34j,  unless  //,  be  etiual  to  //„. 
In  this  case  we  have 

ZT,  cos  0  =  i^cos  (d  ±  0), 

or  II,  =  F(cos  ff  :f  sin  6  tan  0).     .     .     .     (2) 

Hence,  combining  (1)  and  (2),  we  have 

iT,  =  JlXi.  T  tan  ^  tan  0).       ...     (3) 
From  (3)  ff.  can  be  calculated  if  ff.  be  known. 


MAO  NET  ISM. 


157 


If  0  be  ^iiiall  and  iiitiwuml  in  degrees, 

0  X  'T 
tun  0  =   T80~   ^I'P'"^''-' 

and  formula  (3)  becomes 

( 


ir  =  \\  T   0  T^-  tan  if  \  II,. 


(4) 


Practical  Directions.— 1 1 )  A<(/ '(■•<( "i''»f>'  "f  Station  of  Ihf- 
ereiue,  //,._Cai-ctiilly  lev.-l  the  instnunent.  Set  the  zero  of 
the  scale  carried  by  the  magnet  to  one  of  the  quadrant 
divisions  on  the  tixed  scale  immediately  below  it.  Lower  the 
needle  in  the  compass-box  till  it  swings  freely  on  its  i>ivot. 

Turn  the  whole  instrument,  comi)a.>s-box,  and  magnet  to- 
gether, till  the  needle  and  magnet  are  paraHcl,  the  N  pole  of 
the  magnet  pointing  north.  The  exact  position  is  found  by 
turning  till  the  needle  reads  ti»  tiie  <piadrant-point  of  the  box. 

(Mamp  the  box  to  the  stand. 

Now  turn  the  magnet  until  the  needle  is  deflected  just  90°, 
and  set  the  stop  provided  against  the  magnet. 

Reverse  the  needle  by  turning  the  magnet  througli  an 
aiiiilc  on  the  «»ther  si  ie  of  the  meridian  until  the  needle  is 
dctlocted  !*<>°  in  the  opposite  direction. 

Clamp  the  second  stop. 

(2)  AtliuHtinents  ,it  Second  St,itlofi,  7/,.— Take  the  instru 
tnent  now  to  another  stati(»n.  Level  as  before.  Adjust  a- 
before  until  tl  •  needle  and  nmgnet  are  in  the  meridian. 
Without  moving  the  stt)ps,  turn  the  magnet  successively  t.. 
them  and  in  each  case  read  the  dilYercnce  of  the  dertecti.ni 
from  J»o '.  Head  in  each  case  both  ends  of  the  needle,  and 
take  the  Miean  of  the  four  readings  as  0. 

Read  the  angle  through  which  the  magnet  is  turned  from 
the  meridian,  and  take  the  mean  of  the  two  readings  as  ^.  //, 
wi'i'i   iK-  uivator  or  lcs«  thaii    //„  acc-Tding  a;-  the    is'-'-d!'-   in 


158 


LA  BORA  ran  r  physk  's. 


tl«e  second  station  is  (l«>H«'cfo<|  tlironj^li  an  ungle  ^leiiter  or  less 
tlian  9(»  . 

Precaution. — Whoji  oneo  tlic  nia^rnct  lias  been  adjusted  at 
tlie  station  of  rt'tfrt'iu-c,  do  ut  alter  its  po.^itioii  vertically  <»r 
move  the  stops,  otherwise  the  work  will  have  t«>  he  repeated. 

Example — Kiiter  results  thus. 


4 

Htatinn. 

9 

♦ 

iliun. 

S.  Kiid  i>r 
Nemlle. 

- 

5lH;in 
Vnl...  ..r 

0 
-f  3.5.') 

T   4.65 

-  3.65 

U 

Mfi'iillaii. 
X.  Kiiil..f  s.  Ki.il  .if 

.M.ii 
.N.  Kill  of 

Keference 

8<1 
4tli 

3i'  30' 
32'  W 

i                    1 

0              0              0 

f  3  r,  ,    4   3  6       t   3.5 

0 
-t-3.6 

.160 
.156 

,ir>8 

U5 

.Mriin 
Valiif 
32    40' 

■f  4.7       -f  4.7 
-  2.7       -  2.6 

+  4.6 
-  26 

-1-4.6 

-  2.7 

liliiuk  to  he  filled  in  iy  st>i<h')it. 


ELECTRICITY. 


50.   TO  COMPARE  THE  SINE   AND   TANGENT  METHODS 
OF  MEASURING  CURRENTS. 

References— Knott,  pt.  11.  p.  175;  Wutson,  \^\^.  (VsS-tlHT; 
S.  Tlumipsuii,  ).|».  '2()\  and  202;  Carliart,  pt.  11.  p.  3.S5; 
Harkor,  p.  77.'.;  Antliony  and  lirackett,  p.  8.')7 ;  Anies,  p. 
305;  Nichols  and  Franklin,  p.  :{H;  IlaHtinjrs  aiul  IJeach,  pp. 
415-417. 

Apparatus  Required. — A  <;alvanoni»'ti'r  snitaMo  for  botli 
sine  and  tangent  ujctliods;  a  storai^c-ltatterv ;  a  rrsistance- 
box;  a  revurt«inij-key. 

Theory  of  Experiment.— If  (r  he  the  strenfrth  of  magnetic 
tit'ld  at  the  centre  of  a  galvanometer  coil  j)r(iduced  by  a  unit 
ciirrrnt  tiowing  through  the  coil,  then  (r'C  will  be  the 
strenirth  of  ti<ld  for  a  current  6',  the  lines  of  fonte  l)t'iiig  at 
riirlit  angles  to  the  coil. 

Suppose  the  coil  of  the  galvanometer  to  be  in  the  mag- 
netic meridian,  aiid  the  galvantuneter  needle  so  small  that  the 
tield  in  which  it  acts  may  be  considered  uniform. 

Let  M  be  the  magnetic  moment  of  the  needle. 

Then  if  the  needle  be  deHected  through  an  angle  H  by 
tlie  current  (7, 


^;C\f  cos  H  ^   lUl  sin  B, 
where  //is  the  earth's  horizontal  r. .mponent. 


(1) 


150 


sap^'A^ 


160 


Hencci 


LABORATORY  PHYSICS. 
C  =  ^  tan  6*  =  /T  tan  (?. 


(i^) 


If  now,  while  the  current  (7  is  «till  Howinp.  tlic  coil  cf 
the  galvunomotfr  Ikj  turned  roumi,  ful'  'win^'  tlu  nccdk',  until 
the  needle  is  again  in  equilibrium  i  i  n  the  same  relati\(' 
position  to  the  coil  as  it  was  lief  .e  o  r^r  ,  .^g  tunit<l 
on,  then 

GCM  ^  /.  ;,'   ,M  ' 


or 


r  = 


(f,  being  the  angle  through  Wiiieh    I  . 

brii.  r  the  needle  to  its  origiii;il  posin.  ; 

Hence,  eundtiiiiiig  (2)  anti  (;<), 


....     (3) 

iiii  ~    t  'J  turned  to 
•;.■!■'*)  w  to  the  coil. 


or 


sin  6  =-.  tan  0. 


(4) 


5^,--! 


Practical  Directionr —Place  the  eeii  of  the  galvanometer 
accurately  in  the  magnetic  meixlian.  This  may  be  dune  by 
placing  the  coil  so  that  the  needle  reads  zero  on  the  eompa.x.'i- 
box  scale. 

(Connect  in  series  the  galvanometer,  a  resistance-bo.\  .^i.tl 
the  Kiorage-bartery,  j)utting,  however,  !n  the  galvanonjeter 
circuit  a  reversingkey  ^o  that  the  cunent  can  be  rever.sed 
through  tlie  galvanometer.     (See   Fig.  35.) 

In  the  figure  ABCD  is  the  revor.sing-switch,  U  the  gal- 
vanometer, li  the  resistance,  7/,  the  battery. 

By  connecting  .1  to  H,  and  ('  to  />,  the  current  tiv)ws 
through  thegalvaiutnieter  in  one  direction,  and  in  the  opposite 
by  joining  A  to  l\  and  B  to  I). 


/wj>^ 


KLKCIIUCITY. 


161 


rieforo  cloKiuiij  the  oiriMiit  tiiko  out  u  jilii;:  i'roin  tlm  rc- 
6iHturK-e-t)OX  8o  tliiit  jtt  loant  ')<>  oIiiiih  nliiill  la-  in  •',     •rcuit. 

Cloiso  tho  circuit  l»y  iiioaus  of  the  rcvei-.^iiii;  .  irid  ad- 
just tuo  roriistaiice  until  a  tU-JlfCtioa  <>f,  su\ ,  l'>'^  i>  v/Dtuined. 

Ueversc  tlte  current  un<i  read  iiirain. 


G 

T 


Fio.  a.>. 


liotli  ends  of  tho  needle  should  l»e  read  ea.  \\  time  to  tlie 
,\j  of  a  degree. 

Denote  ^lie  angles  hy  ^>, .  .'', ,  ^'j ,  ^, ,  and  the  mean  anglo 
l.y  fi. 

With  tlie  current  still  flowing,  turn  the  galvanometer  coil 
round  its  vertical  axis  until  the  needle  again  reads  r.oxiy.  If 
the  galvanometer  be  i)rn' '  'cd  wit.h  i  >tale  t\»r  measuring 
the  angle  through  which  the  coil  he  turned,  this  angle  can  he 
read  off  directly. 

If  this  he  not  the  case,  wlicn  rhe  needle  rv-.uls  zcio,  open 
the  circuit  and  read  the  angk-  through  v.hirli  it  ^wiiigs  hack. 

Since  in  this  case  the  iummHc  conies  l)ack  to  tiic  iruTidian, 
this  angle  will  he  the  same  as  that  tlirougii  which  th  coil 
was  turned. 

Reverse  the  current,  and  repeat  t!ie  i»peratioii  a-  above. 

Denote  tlie  angles  by  0.  ,  0,,  0,,  0,,  and  the  mean  angle 
by  0. 

Then  by  formula  (4) 

tati  ri  —  sin  0. 


It! 


jg2  LABOR  AWRY  PHYSICS. 

Brin-  the  coil  back  again  to  its  original  position,  and 
adjust  the  resistance  until  thr  re.uling  by  the  tangent  method 
is  approxin.ately  15°,  and  take  the  corresponding  sine  read- 

'"^  Adjust  again  for  20%  25°,  ;'>(>%  and  35%  con.paring  the 
tangents  of  these  angles  with  the  sines  of  correspondu.g 
angles  by  sine  method. 

Record  the  resistance  A'  u  ed  in  each  case. 

Example.— Enter  residts  thus : 


Jj'hid-  to  h,'jil/>'d  In  hy  8i>;<l>ni. 


Mil  4.         1    DirrprciKM". 


I 


ELECTRICITY. 


163 


51.   TO  DETERMINE  THE  ABSOLUTE   MEASURE  OF  AN 
ELECTRIC  CURRENT  IN  AN  INCANDESCENT  LAMP. 


References. — As  in  Experiment  oO. 

Apparatus  Required. — A  tanjjent  galvununieter  (the  coil 
of  wliieli  cun  be  ineasjired) ;  a  pluj;  for  c(>nnectin<j:  with  the 
lighting'  eircuit;  a  portable  incandescent-laini)  stand  ;  a  revers- 
ing-switeh. 

Theory  of  Experiment — If  G  l)e  the  strength  of  the 
magnetic  field  at  the  centre  of  the  galvanometer  coil  dne  to 
a  unit  current,  C  the  current  flowing,  7/ the  earth's  horizontal 
component,  d  the  deHeerion  of  the  needle,  then,  if  the  coil  1 
in  the  magnetic  meridian,  we  have 


)e 


C  =  -,  tan  H. 

Lr 


(1) 


If  ;•  be  the  mean  radius  of  the  coil,  and  /*  the  nnnd»er  of 
turns  of  wire, 


'Inni 


r 


Substituting  in  (1),  we  get 


r 


///■  tan  « 


;,7n 


If  the  current  be  measured  in  amperes, 

1  <•///■  tan  ^t 


0 


L',7// 


(2) 


(Ml 


If    //be   known,  ^  observed,  ui id    /•  measured,  ('<-an    Ij 
calculated. 


164 


LABORATORY  PHYSICS. 


Practical  Directions.— Place  tlie  galvanometer  in  the  mag- 
netic meridian. 

Connect  in  series  the  galvanometer,  the  reversing-switch, 
the  lamp  in  the  portal. le  lamp-stand  and  the  lighting-circ-nit. 
This  is  as:^umiiig  of  conrse  that  the  current  is  a  direct  one. 
A  suitable  furm  ..f  lamp-stand  can  be  made  by  connecting 
two  lamp-s..<'kcts  on  a  board  so  that  the  lamps  can  be  used 

singly  or  in  parallel. 

Put  a  lamp  in  one  socket,  and  turn  on  the  current. 

Kead  the  d"tlection  ol  the  needle  at  both  ends  to  y'o  of  a 
degree,  denoting  the  values  by  f^  and  (^,. 

Uever^e  the  current  ami  read  as  before,  f>\  and  ^,. 

4 


Then 


H  = 


Measure  h}  means  of  a  pair  of  calipers  the  diameter  of  the 
coil.  To  do  this  at  least  three  different  diajneters  for  both 
the  inside  and  outside  of  the  coil  should  be  measured,  and  the 

mean  taken. 

This  mean  diameter  divided  by 'i  gives/-,  the  radnis  of  the 
coil.  The  value  of  //can  be  found  on  a  chart  in  tlie  labora- 
tory . 

Substitute  tlici  values  in  the  formida 


C  = 


1  (>///•  tan  fi 


'2  rr  II 


Measure  tlu-  .-.irrent  thr..ugh  <.ne  It'.-C.P.  lamp,  then 
through  twn  U",-('.P.  lamp:;  in  parallel. 

Then  mea>inv  the  <-urrent  through  two  '.Vl-V .  V.  lamps  in 
parallel,  and  als..  tlirougli  one  Wl-iW.  lamp. 

Finally  tlin.ugh  one  Z'l-V.V.  lamp  and  one  ItJ-C.l'.  lamp 

ill  parallel. 

Precautions,  r.e.areful  not  to  ^hort-(•ir(Mlit  the  hghtmg 
circuit.  Make  all  the  (•unuectioii>  and  be  suw  they  are  cor- 
rect  l)efore  connecting  the  ]>hig  witii  tlie  iamp-sockel. 


BLEcmicirY. 


165 


Example. — Enter  results  thui 


s : 


a" 

^^ 

a/ 

«4° 

i 

Oiltsldt- 
Diaiii. 

Iiisidf 
l)iaiu. 

H. 

Current 
Aiiipa. 

<)ii>*it;-e.i' 

lamp. .. 

«..'. 

0.."i 

1 

lii-vcl>e(l 
TvVM  Id  ('  I- 

lamps. . 

\\.:< 

14.:. 

(!.?< 

fi.V 

t;.r 

.•ii.s 

■■VA.f, 

IT.l 

.48 

( lllf   iJ-C.l' 

lump 

■JU 

^.11 

11  9 

14  :i 

ii.r 

.■il.H 

;«e 

1.03 

i;-vfrs(-il 
Two:;.'*'  i' 

lilllip.s. 

:>ii 

■ii; 

■Ji  1 . ',' 

•M.-i 

■.'•1.1 

31. H 

Ai.C 

1.4» 

K«*V(»fM'u     , 

■Ji 

:ir 

■■'*;  :, 

.ll.S 

3.).0 

■i.M 

Jildiik  ti>  l»    p'llid  in  hij  .sfadtnL 


Oiif  lG-('.r.  lamp. . 

Kfvfrsetl 

Thii  Itj-C.r.  lumps. 

kcverseii    

t)iif  ;!-.•( M'.  lamp  . 

KcviMseil. 

T\vi>  .W  C.l'.  lamps 

Keversed 


Olllsi.l.-     Ill^i.|l 
Ilium    '    \lla\n 


Current 
Aiiip.s. 


i3 


52.  TO  DETERMINE  THE  ELECTRO-CHEMICAL  EQUIVA- 
LENT OF   HYDROGEN. 

References. — Knott,  pt.  ii.  |>n.  I'dU-jixi;  Ilustino's  and 
]>eacli.  J)]..  ;;!tti_4u(»;  AVutMin,  p)..  Tsr.-TSs;  S.  Tliom])son, 
pp.  •JL'l-2-is;  Xicliul-;  ,111(1  Frail l< liii.  pp.  ♦'.7-t;i»:  Ames  p]). 
:',l7-')-22:  AntlK.iiyainl  UiMckftt.  pp.  :]'2:'>~:\2U  \  liarker,  pp. 
741  -74<);    Ciirliart.  pt.  ii.   pp.  -J.").-)   lMIii. 

Apparatus  Required.  .\  taii^imt  ixalvaiioinet' r,  rlio  coil 
<'t  wliicli  can  !»(■  iiH'a.-iirf.i  :  a  i:a<  voltaiiictcf ;  a  resisfancc- 
Ixj.v  ;  a  four-Vdlt  sloraue-hattcrv  or  other  >ource  of  con.>taiir 
ourrent;    a  reversin<r-kf\  ;    a  tla  rnioiiieter. 


166 


LABORATOHY  PHYSICS. 


Theory  of  Experiment. — The  ilectio-clit'iiiical  « '|oivs«i*fnt 
of  u  substance  is  the  nuiss  (tf  the  suhstiiiice  de|K)«iited  by  tlie 
passji{?e  of  a  unit  <|uaiitity  of  electricity  through  an  electrolyte 
in  which  the  substance  is  an  ion. 

If  the  gas  voltameter,  the  battery,  and  the  taiigrnt  gal- 
vanometer be  eonnectetl  in  series,  then  the  current  flowing 
through  the  circuit  is  given  by  the  equation 


//         ^       ///•  tan  ^ 
C  =  V-  ^'">  ^  ^       .>     -    ' 


(.■ 


Snn 


•      (1) 


where  ^is  the  detiection,  //  the  earth's  horizontal  component, 
r  the  mean  radius  of  the  coil,  and  u  the  number  of  turns  of 
wire  in  the  coil. 

If  now,  in  a  time  t'\  theijuantity  of  hydrogen  deposited  by 
the  current,  supposed  constant,  be  //*,  and  the  electro-chem- 
ical e«piivalent  be  denoted  by  t,  then 


Ct"  = 


rii 


therefore 


e  = 


Vt" 


(2) 


Combining  (1 )  and  ('i),  we  have 


e  = 


'2  nil  III 
J/rt"  liiu  t*' 


.     (3) 


If  now  ?«,  the  nuvss  deposited  in  a  given  time,  be  meas- 
ured //be  known,  and  ^  (.liserved,  c  can  be  calculute<l,  /■  and 
n  being  supposed  known  or  nieasunibie  (piantities. 

Practical  Directions,  —('''nnect  in  series  the  galvanometer, 
the  iras  voltameter,  the  battery,  the  rcsistance-bo.x,  and  the 
roversing-switdi.  The  switch  should  be  in  the  galvanometer 
circuit  only,  as  ju  Experinu'iit  .)<»,  1- ig.  ;5o. 


ELECTlilCITY. 


1«7 


leru 
until      suitab 

ail     oxvfft  II  escap 


.u  X 


Unplug  from  the  resistance-box  H»( 

Set  the  i^aivanoiiicter  cuil  carefully 

Close  the  switch,  and  adjust  tlic  ri 
deriection  is  obtaini-d,  viz.,  4;'*"  to  ."id' 

Open  the  >\vitch  and  let  the  liydi 

Now  close  the  key  a<:;ain,  and  take  aiciuutely  the  time  <  f 
starting. 

Reverse  the  current  every  two  juinutes,  and  take  rcatlings 
for  both  ends  of  the  needle.  Denote  the  tirst  readings  by  H^ . 
^, ,  and  the  readings  when  current  is  reversed  bv  ^, ,  H^. 

The  mean  of  the  dctlections  observed  gives  tlie  value  of  H. 

Let  the  current  flow  until  the  tube  containing 
is  nearly  full. 

Take  accurately  the  timt;  at  which   the  curren 

otr. 

Measure  /',  the  radius  of  the  galvanometer  coil. 

liead  the  volume  of  hydrogen  in  the  tube  of  the  voltam- 
eter. 

Take  tiie  temperature,  /,  of  the  solution  in  the  voltameter. 

Kead  from  the  chart  in  the  room  the  aqueous  vapor  j)res- 
sure  for  temperature,  t. 

liead  the  barometric  ])ressiire,  correcting  for  temperature. 

Kead  the  ditfercnce  of  head  between  the  hydrogen  rnd 
the  water  in  the  open  tube. 

If  the  hydrogen  tube  of  the  voltameter  ]»e  not  graduated, 
the  volume  can  readily  be  obtained  a>  follows: 

Let  the  oxygen  e>ca[K'  from  the  oxygen  tube. 

I5y  means  of  a  |)i})ette  or  siphon,  take  the  solution  out  of 
the  open  tubi-  down  to  some  lixe<l  point  just  above  the  upper 
end  of  the  hvdroiren  tul)e.  It  is  ciiuvenient  to  have  a  per- 
mam'ut  mark  on  the  open  or  central  tube  ior  the  purpose. 

Now  let  tiie  hydrogen  CM-ajie. 

Fill  a  graduureu  burette  with  some  oi  the  solutiuii. 


168 


LAUoliA  rati  Y  ru  raicS. 


Let  tlic  solution  tlow  from  the  burette  into  the  voltameter 
until  the  hydroi^en  tube  i.s  just  tilled. 

Close  the  cock  of  the  hydrogen  tube,  care  being  taken  not 
to  let  any  solution  escape  tiirou<j;h  it. 

Fill  the  central  tube  exactly  to  the  marked  point. 

Head  the  burette. 

The  volume  emptied  into  the  voltameter  will  be  oqual  to 
the  volume  of  liyilroj^en  in  the  tui)e  at  the  beginning,  v,. 

In  this  ca.oe  /i  should  be  measured  from  the  marked 
point  to  the  surface  of  the  Iit[uid  in  the  hydrogen  tube  just 
before  it  is  allowed  to  escape. 

To  Jiiul  hi. — To  liiid  the  value  of  //<,  we  nnist  calculate 
the  volume  under  standard  pressure  and  at  o'  ('.,  and  nml- 
tiply  by  the  den>ity  of  hydrogen,  .(((XMKSIMJ. 

If  y.  be  the  volume  of  the  hydrogen  at  standard  tempera- 
ture, (»"  (.'.  or  L'7-'..">  of  the  absolute  scale,  and  under  standard 
]»ressure,  TO  cm.,  <',  the  ol)scrved  volume  at  temperature  t  or 
ti7'2.r)  -f  t  of  the  absolute  scale,  and  under  a  pressure  P,  then 
we  have  the  relation 

n  X  70  i\  X  /* 


27'J.') 


i>72.5  +  t' 


or 


_r^X   /'  X   '^72.5 


(*) 


The  pressure  P'xn  ma<le  up  of  three  parts:  first,  the  baro- 
metric pressure//;  second,  tlie  pressure  (hie  to  the  head  of 
water  in  tiie  voltameter;  third,  the  |.res,>nre  diu'  to  tiie  i)res- 
ence  of  aipu'ous  vapor  in  the  tube  c<.iitaining  hydrogen. 

If  h   Im'  the  dilfercnce  in   heatl    in    the   voltameter,    then 

this  correction  reduced  to  centimeters  ol    mercury  is  - .,  .^^^., 


KLKCTRICtTY. 


169 


of  mercury.  If  the  solution  be  15  jxir  cent,  sulphuric  acid, 
«  =  1.1  approximately.  Assuming  this  to  be  the  case,  we 
have 


'".  = 


/,.   ,    hX  1.1         \ 


TlV-iTli./i  +  O 


(5) 


and  therefore 


7/1  = 


•("+TC5y« -")=<-'-■'*  X- '""'" 


7«K272.5  4-  t) 


-,     •     («) 


01  being  the  aqueous  vapor  pressure  which  can  be  found  for 
the  tt'in|)eruture  t  from  a  chart  in  the  lulutnttory,  or  from  a 
book  of  tables,  and  .O00081H5  the  density  of  hyihogen,  that 
is,  the  mass  per  cubic  centimeter. 

Substituting  this  value  for  m  in  e(]uation  (3),  we  obtain  t\. 

Example  — Enter  results  thus : 

//=.1558.     «  =  30. 


Time  Tirrn- 

of        I         ..f 

Starting.  FinisbiiiK.: 


/" 


B        i 

(iMir.      , 
reeled).  I 


1        1 

1      2.45     I 

3.25 

;• 

h 

15.1 

30.5 

'•i 

I'l, 

;.iH,a 

:s6  :i7 

2400 

t 

1S.() 

V 

.(I0;!'J5!S 


70.02 

1.54 

Itt' 
104 


y: 


170 


LAliOHA  TOR  Y  PH  YSIC'S. 
Blank  to  Ite  Jilletl  in  hy  student. 


•l 

», 

91 

*. 

1 

'rime      1     Time 

■  .f         1          of 

SiiirtlriK-   FiniHliliiK. 

t" 

n 

(cor- 
r«Tte<l.) 

r 

h 

t 

<r 

f) 

ru 

M 

f 
10' 

Mi'UM  vilIiu'  ti 

53.  TO  COMPARE  THE  ELECTROCHEMICAL  EQUIVALENTS 
OF  COPPER   AND  HYDROGEN. 

References. — References  as  in  Experiment  52. 

Apparatus  Required. — A  coi)per  voltameter;  a  gas  vol- 
tameter ;  a  four- volt  storage- battery  or  a  plug  for  the  lighting- 
circuit  ;   a  variable  resistance ;   a  contact-key. 

Theory  of  Experiment. — If  the  source  of  current  bo  con- 
nected in  series  with  a  gas  voltameter  and  a  copper  voltam- 
eter, the  ratio  of  the  eU'ctrochemical  efiuivalents  may  be 
determined  by  determining  the  ma.s8  of  hydrogen  and  the 
mass  of  cojiper  dejxtsited  in  ii  given  time,  and  dividing  the 
one  bv  the  other.  If  ///  be  the  mass  of  hydrogen,  ///,  the 
mass  of  ('oi)i)er,  then 

■  «  ■  •  B  • 

/// 


A* 


(1) 


KLErrmciTY. 


171 


Practical  Directions. — Connect  in  series  a  pop|>cr  voltam- 
eter containing  a  solntion  of  copper  snlpliate;   a  ;^as  voltain 
eter  containinf;  a  ir»-}>er-cent  solution  ot'  sulphuric  acid ;  the 
battery  (or  lightin^'-cireuit);   the   a»lju>'  ''le   resistance;   *he 
contact-key. 

If  the  lighting-circuit  he  used,  a  l(5-caii<lle-pu\ver  lamp 
should  be  in  the  circuic. 

Take  out  the  copper  plate  upon  which  the  copper  i-  to  be 
deposited,  and  thoroughly  clean  it.  This  may  be  dom  y 
washing  in  a  nitric-acid  solution  or  by  rubbing,  when  wet, 
with  emery  paper  and  thoroughly  washing  in  pure  w;i*<"r. 
Dry  the  plate  thoroughly  and  weigh  to  a  milligramme. 

Connect  this  i)late  to  the  negative  pole  of  the  circuit. 

The  negative  pole  nuiy  be  found  by  connecting  the  source 
of  current  to  the  gas  voltameter  alone  and  observing  the  tube 
in  which  the  hydrogen  is  deposited. 

In  iloruif  tliiK,  /loi/'rn  )\  f»^  sutr  fo  /t(ir>  a  yvA/.«'  'nir  (if  not 
lexs  than  lOO  oIdiis  in  thf  ri/viiit  {i(  lO-C.  J*.  hinij>  n,- otlii^r 
reshtanci)  1/  tin'  rHjhtinij-c'urnlt  hr  kshI. 

See  tluit  the  tubes  of  the  gas  vcdtamctcr  are  full  of  the 
solution . 

Close  the  circuit  and  let  it  How  until  the  hydrogen  tidie 
of  the  <ras  voltameter  is  nearlv  full  of  hvdroi,'en. 

Tojind  y/^. — Take  out  the  copper  ])late  upon  which  the 
deposit  has  been  made,  rinse  in  pure  water,  and  dry  and 
weigh  as  before. 

If  w  be  the  weight  before  and  ii\  after  the  deposit  luis 
been  made,  then 


in,  —  a\ 


v\ 


Tojind  in,  the  same  observations  must  be  made  as  in  the 
last  experiment.  The  terms  having  the  same  meaidng  as  in 
that  ease. 


'i  ■ 


172  LABOlLXTuHY  PHYSICS. 

Ax  1.1 


»0,sO<{ 


M 


7t5  x1[^72,6  +  t) 


Precautions.— (1)  Ho  sure  not  to  short-circuit  tlie  liichting- 
circuit  tliroujrh  tlie  y^im  voltameter. 

(2)  Tlic  ck'iim'd  copper  [ilute  mu>t  he  connected  ti»  the 
negative  pole  of  the  suurce  of  current. 

(3)  Thoroughly  chan  an<l  dry  tlic  jilate  each  time  'ifore 
weighing  it. 

Example. — Knter  results  thus: 


w 

75.  KM) 

'"i 

.097 

'•. 

l.W 

35.7 

30.0 

/; 

t 
li 

70.  (C' 

Nl 

.00:il2 

31   10 

liiink  to  hcjilhd  in  hij  Ktiulent. 


to 

1**1 

'"i 

11 

1 

t 

1 

i 

a 

•■i 

m 

H 

KLKCIHICITY. 


173 


54.  TO  DETERMINE  THE  HORIZONTAL  COMPONENT  OF 
THE  EARTH'S  MAGNETIC  FORCE. 

References. — Siiiiic  ns  in  KxjM'rinn'nts  .')!  uiid  .'»2. 

Apparatus  Required.  —  A  taii^cnt  ^'iilvauomt'ti-r,  tho  coil 
of  wliicli  can  he  nicusiit'cit ;  a  copiwr  voltarnotcr ;  a  rcver«iiig- 
key ;  a  storaj;*'  liattcry  ;  an  udjiistahle  resiKtunci', 

Theory  of  Experiment — We  have  seen  that  if  a  current 
How  thrt)U^h  the  coil  of  a  tangent  galvunotueter,  prochicing  a 
deflection,  the  galvanometer  coil  heing  in  the  meridian,  tho 
current  is  given  hy  the  ecjuation 


.,       If,      ^       Jir  tan  fi 

6  =     ,  tan  ff  =  . 

G  'Inn 


Ilencc 


II 


"Inv  cot  H  .  C 
r  ' 


(1) 


n  hcing  the  nunil)cr  of  turns  of  wire  in  the  coil,  and  /•  its 
radius. 

If  now  Che  nioasnrcd  hy  means  of  a  copper  voltameter, 
II can  he  calculated. 

Let  Jf  denote  the  mass  of  copper  deposited  hy  the  pas- 
sage of  the  current  through  the  voltameter,  c  tlie  clectro- 
cheniical  efjuivalent  of  co]iper,  f"  the  time  in  seconds  during 
which  the  current  Hows;    then  as  hefore  (Ex[)eriment  r>2), 

or         ('  =   -:.,.       .     .     .     (2) 


Ct"  =  ^, 
e 


et' 


Hence,  comhining  (1)  and  (2), 

2;r«  cot  H  X  M 


JI  = 


erf 


....     (3) 


m 


MICROCOPY  RESOLUTION  TEST   CHART 

(ANSI  and  'SO  TEST  CHART  No.  2) 


1.0 


I.I 


1^ 

■  30 


IS 


2.2 


1 4.0 


12.0 
1.8 

1.6 


^  /APPLIED  INA^GE    Inc 

S^.  1653  Eost   Main  Street 

r.S  Rochester,   Ne»  York        1*609       USA 

^^S  (716)   482  -  0300  -  Ptione 

^S  (716)   288  -  S989  -  Fax 


174 


LABORATORY  PHYSICS. 


Practical  Directions.—Comiect  iji  series  tlie  tangent  gal- 
vanometer, the  l)uttery,  the  c'up])er  voltameter,  the  reversing- 
key,  and  an  adjustable  iesistan(;e. 

Put  tlie  reversing-key  in  the  galvanometer  circuit  only 
(Kig.  35). 

Close  the  circuit  and  adjust  the  resistance  until  a  suitable 
deHection,  about  45°,  is  obtained,  the  coil  of  the  galvanom- 
eter being  in  the  meridian. 

A  meter  or  two  of  bare  German-silver  wire,  No.  20, 
makes  a  suitable  resistance  and  can  be  adjusted  at  one  ter- 
minal of  the  battery. 

Now  open  the  circuit  and  take  out  the  plate  upon  which 
the  deposit  is  to  be  made.  Clean,  dry  and  weigh,  as  in  the 
last  experiment,  and  restore  the  })late  to  its  place  again. 

Ee  sure  that  the  negative  pole  of  the  battery  is  connected 
to  the  clean  plate,  otiierwise  copper  will  be  taken  off  in- 
stead of  being  deposited  upon  it. 

Close  the  circuit,  taking  accurately  the  time  of  closing. 

Let  the  current  How  for  3(»  minutes  or  moie. 

Take  accurately  the  time  when  the  current  is  turned  off. 

While  the  current  is  on,  reverse  everv  two  minutes  and 
read  deflections,  reading  always,  if  possible,  both  ends  of  the 
needle,  denoting  the  four  readings  by  6^, ,  ^, ,  6^, ,  6^. 

The  mean  of  these  gives  the  true  value  of  d. 

Unless  a  rapidly  reversing  commutator  is  used,  the  time 
of  each  reversal  should  be  taken  and  allowed  for. 

Take  again  from  the  voltameter  the  plate  upon  which  the 
copi)er  deposit  has  been  made. 

Wash  the  plate  by  letting  pure  water  flow  gcntky  over  it, 
or  l)y  rinsing  in  a  10  i)er  cent,  solution  of  sulphuric  acid. 

Dry  as  before  by  holding  it  neat'  a  Bunsen  flame. 

Weigh  the  })late. 

The  difference  between  the  two  weights  is  the  copper  de- 


ELECTRICITY. 


175 


posited.    Measure  the  radius  of  tlie  coil  as  in  previous  experi- 
ment. 

The  electro-chemical  equivalent  of  copper,  7i',  is  .Uo;}28C. 

Example. — Enter  results  thus : 


e. 

., 

9, 

46.5 

46.0 

46  7 

46.2 

45.8 

46  ;{ 

46.3 

46  1 

46.5 

46.3 

46.0 

46.5 

46.1 

45.9 

46.3 

46.2 

45.9 

46.3 

46.1 

45.7 

46.2 

46.3 

45.9 

46.1 

46.1 

46.1 

40.3 

Mean  value,  0. 


46.3 
46.2 
46.3 
46.3 
46.2 
46.2 
46.3 
46.3 
46.1 


46.2 


w 

Time  of 
istartiiig. 

n 

250.700 

2.35 

30 

"'. 

Time  of 
Finisliiiig. 

r 

250.748 

30.5 

15.1 

J/ 

t" 

1 

// 
.147 

.048 

1200 

Blank  to  he  filhd  In  hj  Ktudent. 


Mean  value,  0 


ir, 


1  M 


Time  of 
Siariiiit;. 


Time  of 
FinisliiiiK. 


// 


176 


LABORATORY  PHYSICS. 


55.    TO   DETERMINE   THE    REDUCTION   FACTOR  OF   A 

GALVANOMETER. 

References. — As  in  Experiment  54, 

Apparatus  Required. — A  tangent  galvanometer;  a  gas  or 
copper  voltameter ;  a  storage -battery  or  plug  for  the  lighting 
circuit;  an  adjustable  resistance  capable  of  carrying  one-fifth 
of  an  ampere ;  a  re  versing- switch. 

Theory  of  Experiment. — The  theory  of  this  experiment  is 
exactly  the  same  as  the  last,  the  only  difference  being,  that  in 
this  case,  since  the  value  G  cannot  be  directly  measured,  the 

value-—,  the  "reduction  factor,"  is  obtained. 


Since      C 


— r  tan  5  =  ^tan  8, 
(r 


K  —  C .  cot  e 


(1) 


Practical  Directions. — The  connections  and  observations 
are  exactly  as  in  the  last  experiment. 

If  a  gas  voltameter  be  used,  observations  similar  to  thoso 
in  finding  the  electro-chemical  equivalent  of  hydrogen  must 
be  made. 

If  the  current  be  taken  from  the  lighting  circuit,  a  lamp 
should  always  be  in  series  with  from  500  to  900  ohms  resist- 
ance. An  ordinary  resistance- box  is  not  suitable,  as  the  coils 
are  liable  to  burn  out.  A  coil  made  from  No.  24  or  25 
German-silver  wire  serves  the  purpose. 

In  the  case  recorded  below  a  gas  voltameter  was  used. 


m 


ELECTRICITY. 
Example. — Enter  results  thus: 


177 


» 

Mfttii. 
40°  18' 

t" 
3840 

B 

h 

t 

a 

V 

C 

. 

76.75 

35.0 

17 

1.44 

38. 2S 

.0837 

.080 

lilanJc  to  le  filled  hi  hy  student. 

Mfcin. 

t" 

B 

li 

/ 

a 

V 

c 

a: 

56.  TO  PROVE  OHM'S  LAW,   C 


E 


References.— Knott,  pt.  11.  pp.  184-187;  Watson,  p. 
688 ;  Barker,  p.  699 ;  S.  Tlioiiipson,  pp.  1 75  and  397 ;  Has- 
tings and  ]ieacli,  p.  395;  ^Nichols  and  Franklin,  vol.  11.  p. 
54;   Anthony  and  Brackett,  p.  317;   Ames,  p.  333. 

Apparatus  Required.— A  tangent  galvanometer  (prefer- 
ably one  sensitive  to  fairly  small  currents);  a  storage  battery; 
a  resistance-box ;  a  reversing-switch. 

Theory  of  Experiment.— If  the  galvanometer,  the  lesist- 
ance-box.  an<l  the  source  of  current  be  connected  in  series 
then  the  relation  between  current  and  deflection  is  given  by 
the  equation  r  =  A'  tan  H. 

Further,  by  Ohm's  Law, 

E 


ir   _J 


C'  = 


u: 


178 


LABORATORY  PBISICS. 

E 
Kt&n0=  ^. 


Hence 

K  is  constant,  E  is  constant  if  a  storage  battery  be  used ; 

hence  ^i  -  j^^» 

where  a  is  a  constant. 

Suppose  a  series  of  values  of  (f  be  observed  for  different 
values   of  L\  and   a   curve   plotted,  with  B   for   abscissas 

and 


_i^  for  ordinates;  then  if  C-  ^,  the  curve  will  be  a 
tan  H  ^ 


straight  line. 

Practical  Directions.— Connect  in  series  the  galvanometer, 
the  storage  battery,  the  resistance-box,  and  the  reversing-key, 
the  galvanometer  coil  being  carefully  placed  in  the  meridian. 

Unplug  a  large  resistance  from  the  box. 

Close  the  circuit,  and  adjust  the  resistance  until  a  deflec- 
tion of  about  10°  is  obtained. 

Read  the  resistance,  Ji,  and  the  deflection,  0,. 

Revei-se  the  current,  and  read  again,  ^,. 

The  mean  value  of  the  deflections  gives  0. 

Dimitiish  the  resistance  in  the  circuit  until  the  deflection 
is  about  15°,  reverse  and  read  as  before. 

Change  the  resistance,  obtaining  deflections  as  nearly  as 
possible  to  20%  25%  30°,  35°,  40°,  45°,  50°,  55°,  reading 
corresponding  values  for  the  resistances. 

Plot  a  curve  for 7.  ^^^  ^  ^^  indicated  above. 

tan  c/ 

It  will  be  noticed  that  the  line  does  not  pass  through  the 
origin.  This  is  because  the  resistance  of  the  galvanometer 
and  battery  lias  been  neglected  in  plotting. 

If  the  line  he  produced  to  cut  the  axis  of  abscissas,  the 
jjetrative  abscissa  will  obviously  be  the  resistance  of  the  gal- 
vanometer  and  battery. 


In-' 


-Ts^r*»*».:ft>'»^TT.*.A»i*  -^.rK-^ChT.^^-.*^* 


ELECriilCITT. 


179 


Precautions. — Before  coiiiiectirii^  itj  the  battery,  be  sure 
to  unplug  a  large  resistance  from  tlie  box. 

Never  have  less  than  20  ohms  in  the  circuit,  unless  the 
resistance-box  is  known  to  be  suited  for  (  urrents  used. 

Example. — Enter  results  thus: 


Blank  to  he  filed  in  hy  student. 


•. 

9i 

« 

tan  9 

1 
tan  • 

R 

57.    COMPARISON    OF    ELECTRICAL    RESISTANCES   BY 
MEANS  OF  A  SINE  OR  TANGENT  GALVANOMETER. 

References. —  Knott,  p.  1!)7;  Watson,  p.  ♦>ss ;  Barker, 
]).  7<>(>;  Hastings  and  Beach,  pp.  425-420;  Nichols  and 
Franklin,  vol.  ii.  p,  !>1  ;  S.  Thompson,  p.  413;  Anthony  and 
Bruckett,  pp.  319  and  860;    Ames.  pp.  333-H;J7. 


hi 

W 
if, 

r...'k 


180 


LAUOIiATOHY  PHYSICS. 


Apparatus  Required.- A  sine  or  tnnjrent  frulvanometer ;  a 
resistance-box;  a  storugo  Lattery ;  a  reversing-switch,  resist- 
ances to  be  measured. 

Theory  of  Experiment.— If  a  <ralvanonieter,  a  known 
resistanee  h\  an  unknown  reMstanee  A',  and  a  battery,  be  con- 
nected  in  series,  from  Olim's  Law, 


(1) 


A' 

C rr  T— 1'  =  A' tan  6     . 

if  the  galvanometer  be  a  tangent  galvanometer, 
Qf  =  K  m\  0 

if  it  be  a  sine  galvanometer,  B  and  G  being  the  resistance  of 
the  battery  and  galvanometer  respectively. 

If  now  the  re^^ir^tance  X  be  removed  from  the  circuit,  and 
R  adjusted  to  A*,  so  as  to  give  the  same  dcHection  as  before, 


then 
or 


B-\-G  +  li  -\-  X  =  7?  +  6  +  /i'., 
X=  li,-  li 


Ci) 


It  is  usually  impossible  to  adjust  the  resistance  R,  so  as  to 
get  the  same  detlcction  exact!  • 

If /i*,be,  therefore,  a  resistance  which  gives  a  deflection  W,, 

^'  =  A' tan  fi,.  .     .     .     Co) 


then 


Hence 


a  =  ,T- 


li  +  G  +  B, 
tan  e  __       IJ+  G  ±J?, 


wmbinuig  (D  uiid  (:'.)• 

If  ji  _|_  ^;,  A'  and  A',  be  known,  tf  and  0,  observed,  A  can 

be  calculated.  ^  ,     ,  .   i  *i 

UB+G  be  not  known,  they  can  be  hrst  calculated  thus . 


•«.  ^"w.*  .•'fST  «#K»'=^'  'iWAl^  t?am»-  <^  ^.^h  \.k    ^bv*  ^•^^Tj/km^^^i;^^-  «>w«t' 


BLBCTRICIT7. 


181 


Using  equation  (3), 


E 


Changing  R^  to  ^,,  we  get 

E 


=  K  tan  ^,. 


=  K  tan  ^,. 


Hence 


B  +  G  -\-  n^  _  tan  g, 
i?  4-  6^  +  A*.  ~  tan  ^,' 


or,  denoting  B  -\-  G  by  J', 

r  +  K 


tan  ^. 


1'  +  li,       tan  6^,' 


(4) 


from  which  Y  can  at  once  be  calculated. 

Practical  Directions C-onnect  in  series  the  resistance-box, 

the  battery,  the  galvanometer,  and  a  reversing-switch. 

Before  closing  the  circuit  unplug  from  the  box  a  large  re- 
sistance. 

Set  the  galvanometer  coil  accurately  in  the  meridian. 

Close  the  circuit  and  adjust  the  resistance  until  the  deflec- 
tion is  about  ."0°.     Denote  reading  by  S. 

Reverse  the  current  and  read  again,  d,,  taking  the  mean  as  B. 

Adjust  the  resistance  again  until  a  deflection  of  about 
00°  is  obtained. 

lieverse  and  read  a.s  Ijefore,  ^,,  rf, ,  taking  the  mean  as  6*,. 

From  these  observations  calculate  B  +  G. 

Now  put  in  the  unknown  resistance  A",  and  adjust  the  re- 
sistance in  the  box  until  the  deflection  is  again  about  60°. 

Use  this  observation  with  the  flrst  (30")  to  calculate  the 
value  of  X. 

Tlepeat  the  operation  for  three  or  four  different  resistances. 


182 


LAJiORATORY  PHYSICS, 


If  a  sine  givlvanonieter  he  u»M'd,  Kuhstituto  m\  8  fur  tan  f)  in 
all  till'  ctilculatioiis,  but  the  detlcetions  must  hv  tukm  in  uc- 
cordunce  with  tiie  hiiiu  method,  see  Experiiiieiit  ;")(). 

Example. — Enter  results  tliiis: 


i 

«. 

« 

<. 

*. 

»i 

K 

1 

80. 

31.8 

30.7 

63. 

61. 

62. 

30 

9 

11.4 

12.0 

11.7 

11.2 

11.8 

11.5 

30 

89 

2«.6 

26.0 

26.7 

27.0 

27.4 

27.2 

30 

37 

n  t  (I 


57.0 

4  .  I 


Blank  to  hejilled  in  hy  stu</ent. 


t 

«. 

$ 

«. 

«• 

». 

i? 

II, 

B  k-U 

X 

58.    TO   MEASURE    ELECTRICAL    RESISTANCES  BY  A 
B.  A.  WIRE  BRIDGE. 


■'  i 


References.— Knott,  p.  198;  Watson,  pp.  604  and  095; 
S.  Tiiompson,  p.  415;  Hastings  and  Beach,  pp.  433  and 
434;  Nichols  and  Franklin,  vol.  11.  ]).  93;  Anthony  and 
Brackett,  pp.  361  and  362 ;   Ames,  p.  337. 

Apparatus  Required.— A  R.  A.  bridge;  a  battery;  a  low- 
resistance  galvanometer;  a  resistance-box;  a  contact-key; 
resistances  to  be  measured. 


EI.KniWllY. 


183 


Theory  of  Experiment.— If   an    electric  current   C  tiow 
through  a  conauctor  /.',  thou,  by  OhnrH  law, 

E 


C  = 


R' 


E  being  the  E.  M.  F.  of  the  source  of  current. 

Hence  the  K.  M.  F.  between  any  two  jwints  on  the  con- 
ductor is  j)roi)ortional  to  the  rertistance  between  these  points. 

If  a  Ktiotched  wire  be  connected  in  parallel  with  two 
resistances  wliicli  are  in  series,  and  a  current  How  thn.uj^di^ 
the  whole,  as  per  diagram,  vl  A' being  the  wire,  AC  and  Ck 


the  resistances  i?  and  i?.  respectively,  r  \  B  ti  hattery,  then 
the  difference  of  potential  between  liie  |  ^  ^  «"^  ^' '^ 
the  same  whether  we  consider  the  path  A('K 


ADK. 


Hence  when 


AK  _  RA-_R, 
AD~       R      ' 


or 


DK 
AD 


R' 


the  points  D  and  Care  at  the  same  potential  a 
no  current  will  How  through  a  galvanometer  n 

D  and  C. 

Resistance  of  T>K        „ 

In  this  case       /t,  =  ^ — ^.  -  7~T7i  ^ 

'        Kesistance  ut    W 


.      .     (1) 

the  if  fore 
•cteU    ^o 


,i 


fl 


'  ,.^     m.  ^MJ^^iC4J.  , 


Ib4 


LA  ItnUA  T<Ht  Y   I'll  YSli  .s'. 


If  li  be  u  ktutwii  resistuiicr,  J  A'  ii  iiiiifttrm  wire,  •  ul  a 
jM»int  I)  l»e  t'i»unil  in  it  so  that  no  detlectioii  i»f  a  i^uivanom- 
eter  takes  place  when  l>  and  C  are  conneete*!  thron^li  it, 
then  if  the  lengths  All  and  Jih'  Ite  nieasnred,  It^  can  l)e  eaU 
euhited. 

Practical  Directions. — Tiio  U.  A.  inidge  consists  of  a  uni- 
form wire  AH  stretched  against  a  centimeter  wale  so  that 
the  lengths  of  the  segments  of  the  wire  can  he  read  off  at 
onee.  It  is  provided  with  terminals  tor  eonneeting  in  the 
resistances  to  he  measnred,  the  standard  resistance,  and  the 
battery. 


Fig.  37. 

Connect  tlie  standard  resistance  and  tlie  unknown  resist- 
ance in  the  bridge,  as  in  Fig.  37. 

Connect  the  battery,  B,  through  a  contact-key,  K,  to  tlie 
tenninals  })rovided  for  the  purpose. 

Connect  the  point  between  the  two  resistances  to  the 
galvanometer,  and  through  the  other  terminal  of  galvan- 
ometer, (r,  to  the  sliding  contact,  *S'. 

Close  the  battery  circuit  first  and  then  press  lightly  the 
sliding  contact  on  the  wire :  the  galvanometer  will  be  de- 
flected. 

Adjust  the  jiosition  of  the  contact,  repeating  the  opera- 
tion until  no  deHtM'tion  is  (>l>tai!i(M|, 


V^  'l     'm..~a^'W- 


KLKCTHIVITY. 


Ls;. 


The  standard  rcHiHtanco  should  bo  a  one-ohm  box  (Uvulud 
in  tentlis,  and  the  rt'Histancu  sliould  bo  udjusti'd  so  that  tho 
bahince-i)oint,  tV,  iw  near  tho  middle  of  tho  wire. 

Having  fonnd  tho  balunco-point,  road  tho  iongtiis  <tf  tho 
Rogmonts  of  tho  wire. 

Calculate/^,. 

Tho  inothiKl  is  o\\\y  suitable  for  mearturing  bmall  resist- 
ancetj. 

Measure  tlio  resistances  of  tlie  given  coils. 
Example. — Enter  results  thus: 


SH 

-«. 

50.8 

1.08 

54.5 

1.55 

51.3 

2.42 

33.8 

4.89 

Blank  to  he  jilhd  in  hy  stmhnt. 


R 

AS 

SH 

«i 

\ 

59-  TO  MEASURE  ELECTRICAL  RESISTANCES  BY  MEANS 
OF   A  DIFFERENTIAL  GALVANOMETER. 

References. — As  in  last  Experiment,  and,  in  addition,  S. 
Thoiiip.son,  pp.  207  a)id  413. 

Apparatus  Required — A  differential  galvanometer;  a 
battery;  a  standard  resistance-box  divided  to  tenths;  resist- 
ances to  be  measured. 


186 


LABORATORY  PnTSICS. 


Fig.  88. 


Theory  of  Experiment.— A  differential  galvanometer  is  one 
l)rovi(led  with  two  coils  exactly  siniilar  in  construction  placed 
symmetrically  with  reference  to  the  magnetic  needle,  so  that 
the  needle  will  be  uninfluenced  by  equal  currents  flowing  in 
opposite  directions  through  the  coils. 

Let  VI) C,  and  CEO,  represent 
the  two  coils  of  equal  resistance, 
^''symmetrically  placed  with  regard  to 
the  needle,  h*  and  li,  two  resistances 
in  series  with  the  coils  (DO,  and 
CAV,  reo[)ectively. 

If  if  and  /*  be  connected  through 
a  battery  B,  the  cui  r-nt  will  flow  through  the  coils  in  the 
directions  indicated  by  the  arrows. 

Since  CBG,  =  CEC„  and  equal  currents  throngh  them 
will  produce  no  deflection,  then  no  deflection  will  be  obtained 
when  /?  =  /i*,. 

If  R  be  a  standard  resistance,  H^  is  directly  measuied. 

Practical  Directions The  following 

figure  shows  the  connections  for  one 
type  of  instrument,  C,  Z,  7*,  Q,  /*, ,  Qi 
being  terminals  to  which  connections  are 
made.  C„  the  middle  point  of  the  coils,  ( 
is  connected  to  one  pole  of  the  battery, 
the  other  ends  of  the  coils  being  con- 
nected to  P  and  P,  and  through  them 
in  series  with  H  and  li,  respectively. 

The  other  pole  of  the  battery  is  con- 
nected  through  C  and  the  contact  K  to 
the  middle  point  of  R  ;ind  R,. 

When  ^is  closed  the  current  divides,  going  through  Ji 
and  li,  and  the  coils,  as  indicated  by  the  arrows. 

To  test  the  coils  of  the  iralvanoraeter,  adjust  /t,  *he  stand- 


FiG.  39. 


ELECrmClTY. 


187 


ard,  until  no  deflection  is  obtained.  Then  interchange  R  and 
A',  and  close  the  circuit.  If  now  no  deflection  be  obtained, 
it  may  be  assumed  that  the  coils  are  equal  ai\d  accurately 
placed. 

To  measure  resistances  to  the  second  place  of  decimals,  it 
is  necessary  to  interpolate  by  taking  deflections  on  either  side 
of  the  zero  for  differences  of  one  tenth  in  li. 

Example. — Enter  results  thus : 


R 

Deflections. 

100.04 

175.25 

75.40 

jlOO 

noo.i 

i  175.3 
j  175.3 
(   75.4 
(  75.5 

+  21 

zl\ 

+  3 
-3> 

+  2^ 

Blarih  to  he  Jilhd  in  hi/  student. 


R 

Deflections. 

ff. 

I  !  ! 


188 


LABORATORY  PHYSICS. 


60.  TO  PROVE  THAT  THE  RESISTANCE  OF  A  WIRE  IS 
DIRECTLY  AS  ITS  LENGTH,  AND  INVERSELY  AS 
THE  CROSS-SECTION;  AND  TO  FIND  THE  SPECIFIC 
RESISTANCE  OF  A  WIRE. 

References. — Anthony  and  Brackett,  p.  319;  Carhart, 
pt.  II.  p.  275:  Knott,  pt.  11.  p.  181);  S.  Thompson,  p.  402; 
Barker,  p.  700;  Ames,  p.  333;  Nichols  and  Franklin,  vol. 
II.  p.  49:  Watson,  p.  689. 

Apparatus  Required.-- -A  B.  A.  Bridge;  a  sensitive  gal- 
vanometer; a  standard  resistr nee-box;  a  battery;  a  contact- 
key. 

Theory  of  Experiment. — If  I  and  I,  be  two  lengths  of  wire 
of  the  same  material  but  of  different  diameters,  then  the 
resistance  of  the  lirst  is  given  by  the  equation 


/i'  = 


4pZ 


I.' 


that  of  the  second  by       7?,  = 


assuming  that  the  resistance  is  directly  as  the  length  and  in- 
versely as  the  cross-section,  p  being  the  specific  I'esistance,  d 
and  dj  the  diameters. 


Hence 


d^ 
dX 


.     .     (1) 


If  now  the  ratio  R/Ii^  be  measur-ed  directly  by  means  of 
the  B.  A.  bridge,  equation  (1)  can  be  verified. 


ELECTRICITY. 
Having  verified  tlie  relation,  since 

It  —    -T,J 

na 


189 


we  have 


=  li 


il' 


I^Feasiu-ing  li  directly  by  means  of  the  standard  resistance 
end  B.  A.  bridge,  we  calculate  p. 

Practical  Directions. — Take  a  meter  or  so  of  German- 
silver  wire  about  Xo.  IM  and,  with  a  draw-plate,  draw  part 
of  it  down  to  about  So.  30. 

Coil  the  two  parts  together  and  anneal  them  thorouglily 
in  a  gas-flame,  to  bring  them  to  the  same  specific  resistance. 

Solder  the  ends  of  the  wires  to  short  thick  copper  con- 
nectors. 

The  wire  with  the  smaller  diameter  should  be  made 
shorter  than  the  other,  so  as  to  make  their  resistances  nearly 

equal. 

Measure  carefully  by  means  of  a  meter  scale  the  lengths 
of  the  wires,  and  the  diameters  by  means  of  a  screw-gauge. 

Calculate  the  ratio,  Ii/B,,  by  means  of  tMiuatioii  (1). 

Tsow  connect  the  two  wires  in  the  arms  of  the  I>.  A. 
bridge,  and  adjust  until  no  deflection  is  obtained  on  making 
contact  with  the  sliding  c«.>ntact  of  the  liridge.  The  ratio  of 
i?to  A',  is  obtained  directly  from  the  ratio  of  the  two  lengths, 
a  and  a,,  of  the  bridge  wire,  or  /«'//«',  —  ot/n!,- 

liemuve  one  of  the  wires  from  the  l)n<lge,  and  in  its  place 
put  the  standard  resistance. 

Measure  the  resistance  of  the  other  wire  by  the  ordinary 
li.  A.  bridge  method. 

The  standard  resistance  should   be  divi<led  in  tenths,  so 


190 


LA  BORA  TOR  Y  PHYSICS. 


•t 


m 


that  a  resistance  approximately  tlie  same  as  the  wire  can  be 
unphigged  from  it. 

This  observaJon  gives  the  vahie  U. 

Calculate  /j. 

Rei)cat  the  observation  for  tlie  second  piece  of  wire  and 
calculate  p  again. 

Example. — Enter  results  thus : 


To  verify  Law. 


To  calculate  p. 


I 

'. 

d 

.092 

i? 

a 

»i 
52.8 

52.5 

.000016 
.OOOOlob 

100 

232 

aj 

49.7 

.061 

50 
50 

47.2 
47.5 

a 

rf". 

1 
,        1 

50.3 

1.02 

1.01 

■  It  I 


Blank  to  he  filed  In  hy  Kfiuhnf. 


dVj 


>'l    i 

fi 

a/ a.  I 

1 

*  i 


fl 


ELECTRICITY. 


191 


6i.  TO  MEASXIRE  THE  RESISTANCE  OF  A  GALVAN- 
OMETER BY  SHUNTING  WITH  A  KNOWN  RESIS- 
TANCE. 

References.— Ames,  p.  335 ;  Watson,  p.  693 ;  Hastings 
and  Beacli,  p.  429;  S.  Thompsoni,  p.  409;  Barker,  p.  705; 
Nicliols  and  Franklin,  vol.  in.  p.  56  ;  Antliony  and  IJrackett, 
p.  361;  Carhart,  pt.  ii.  p.  276;  Knott,  pt.  ii.  p.  190. 

Apparatus  Required. — A  galvanometer ;  a  coil  for  shunt- 
ing; a  resistance-box;  a  battery  of  constant  E.M.F. ;  a  re- 
versing-key 

Theory  of  Experiment. — If  a  resistance  R,  a  galvanometer 
of  resistance  6',  and  a  battery  with  an  E.M.F.  if  and  negligible 
resistance,  be  connected  in  series,  then  the  current  C  is  given 
by  the  equation 


C  = 


E 


or 
or 


If  0  be  the  deflection  of  the  galvanometer,  then 
C  =  K  tan  e, 
=  K  sin  e, 
=  Kd, 


according  a*  the  galvanometer  is  a  tangent,  sine,  or  reflecting 
instnnnent,  \\\  tlie  latter  ca^e  ^  being  the  scale  deflection. 
Hence,  taking  the  second  case, 


h 


ir^ra-^^^- 


(1) 


If  now  the  <riilv,ui(>rnet(  r  he  sinnitod  by  means  of  a  coil  S", 
the  other  conditions  remaining  the  same,  by  the  tlieory  of 


192 


LABORATOBT  PHYSICS. 


Bhunts  the  total  current  in  the  circuit  is  given  by  the  equation 


a  = 


E 


and  the  part  of  the  current  through  the  galvanometer  by  the 
equation  ^  _        ^ 


Hence 


C   — 


F 


s 


R  + 


or 


.     .     (2) 


^»  '-  Ii{G  -\-  ^)  +  GS' 


(3) 


But  C\  is  also  ecjual  to  K  sin  0„  6,  being  the  deflection  of 
the  galvanometer  in  this  case. 


Dividing  (1)  by  (4),  we  have 

^(r;  +  j^^)  +  OS  _  sin  ^ 

'7?(/r+  ay    -  ^huT^  ■ 

Denoting  the  ratio  V  -^-  l)y  r,  and  solving  for  G,  we  obtain 


.      .     (i) 


.     (5) 


r/ 


7^%  -  1) 


(<0 


from  which  G  can  be  calculated. 

If  the  galvanometer  be  a  tangent  instrument,  substitute  for  /• 

tan  0 


tan  fl. 


ELECTRICITY. 


103 


If  tlie  galvanometer  be  a  sensitive  reflecting  galvanometer, 
equation  (1)  becomen 

A' 

(7) 


Ks  = 
and  (2)  becomes 

KS,  = 


Ji  +  6" 


S 


Ji 


(JS    X  (/+  ^'   •    •    •    (^) 


■^  (T-i-^ 


In  the  case  of  a  retlectiiig  galvanometer,  however,  li  is 
generally  so  large  as  compared  with  G  that 

s+o +  .<='''+''' 

to  a  close  approximation. 

Ill  this  case,  therefore,  dividing  (7)  by  8  we  obtain 

6_G-i-S 
6.  ~ 


or 


G  = 


(») 


It  is  usually  more  convenient  to  shunt  the  galvanometer 
for  both  observations. 

In  this  case  equation  (7)  becomes 


K6  = 

equation  (8)  become 


s 


B.+ 


C/ -t-  S  ^  'S  +  G ' 
GS' 


(10) 


E 


X 


s. 


GS^  G  ^  S,' 


(11) 


104 


LABORATORY  PUYHlCS. 


mi' 


Assuming  now  that 
2i  + 


we  obtain 


6 


OS 


=  li-V 


GS, 


G  4-  ^: 


S{G  +  j».) 
b\{G  4-  S) 


Denoting  v  '  7  r  we  obtain  on  solving  for  G 


(12) 


Practical  Directions. — (1)  -AW  fSineor  Tangent  Galvanoin- 
eter. — Connect  in  series  tbe  buttery,  the  resistance-box,  and  the 
galvanometer,  putting  in  the  reversing-key.  A  sn)all  storage- 
battery  is  most  suitable,  since  it  has  a  steady  E.M.F.  and 
practically  no  resistance. 

Connect  the  shunt  coil  to  the  tenninals  of  the  galvanometer, 
putting  a  contact-key  in  the  circuit  (see  Fig. 
40). 

Place  the  galvanometer  in  the  meridian. 
If  a  sine  or  tangent  galvanometer  witi»  sus- 
pended needle  be  used,  care  must  be  taken  to 
eliminate  torsion.  To  do  this,  lay  down  the 
meridian  by  means  of  a  compass-box  and  turn 
I  the  torsion-head  of  the  needle  until  the  needle 
lies  in  the  meridian. 

Now  unplug  a  large  resistance  from  the 
bi>x  R,  and  close  the  circuit  by  means  of  the 
reversing-key  A'  lea\ing4lie  shunt  circuit  open. 

Adjust  the  resistance  R  until  a  suitable  deflection  is 
obtained,  about  35°,  before  turning  the  galvanometer. 

Turn  the  giilvauonietcr  until  the  needle  again  reads  icero, 


Fig   40. 


ELECT1UCIT7. 


115 


that  is,  occupies  tilt'  same  relative  position  to  the  coil  as  before 
closing  the  circuit. 

liead  the  aiijjle  thruugh  which  the  j^ah  aiioiueter  was  turned. 
If  the  galvanometer  he  not  provided  with  a  .scale  tor  reading 
otf  directly  the  angle  through  which  it  was  turned,  then,  after 
bringing  the  needle  to  zero  with  the  current  on,  open  the  key 
and  read  the  angle  through  which  it  .swings  back.  This  will 
i»L'  the  dericction  for  the  sine  method. 

If  a  tangent  galvanometer  be  used,  adjust  the  resistance  H 
until  a  dericction  of  above  t'»0°  is  obtained.  IJeverse  the  cur- 
rent ai.d  repeat  the  observation,  denoting  thi-  mean  reading 

bv  t). 

Now  close  the  shunt  circuit  simultaneously  with  the  battery, 
liepeat  the  observations  as  before,  denoting  the  mean  reading 

Find  from  the  tables  sin  H  and  sin  «,. 

Substitute  the  value  /■(' .     ^  ]  with  the  values  for  R  and  S 

Vsm  ^i) 

in  ccpiatioii   (»'»),  and  calculate  <}. 

Kepeat  the  observations  three  times. 

{•!)  Far  a  Rffednuj  (Jdlranonicter. — It  \'ill  be  necessary 
to  caref idly  adjust  the  galvanometer  in  this  case  if  this  be  not 
already  done. 

First  carefully  level  the  instrument  by  means  of  the 
levelling-screws  attached. 

Adjust  carefully  the  height  of  the  needle  by  means  of  the 
sus})ension-head  until  the  centre  of  the  minor  is  appro.xi- 
nuvtelv  at  the  centre  of  the  aperture  in  the  C(jil  through  which 
the  light  is  admitted. 

If  the  needle  be  properly  susi)ended,  it  will  now  swing 
tVeclv.  A  little  further  adjustn.ient  of  the  levelling-hcrews  may 
be  necessary. 


196 


LA noilA  TOR T  PIITSICS. 


t'  x  1! 


,ij|S' 


Place  tlio  lamp  (uid  scale  in  front  of  the  mirror,  at  a  dis- 
tance of  about  H  meter,  and  adjust  the  position  of  the  scale 
until  the  line  joiniiij;  its  centre  with  centre  of  the  coils  is  at 
right  angles  to  the  plane  of  the  coils,  and  its  plane  parallel  to 
the  plane  of  the  coils. 

By  means  of  the  control  magnet  adjust  the  pv)sition  of  the 
mirror  and  needle  until  the  light  is  retlected  from  the  mirror 
towards  the  scale. 

The  position  of  the  retlected  light  can  he  determined  by 
liolding  a  sheet  of  white  paper  in  front  of  the  mirror.  The 
height  of  the  scale  can  then  he  adjusted  until  it  receives  the 
reflected  image. 

Vary  the  distance  between  the  galvanometer  and  scale  until 
a  clear  image  is  obtained.  If  the  centres  of  the  mirror  and 
scale  be  in  a  line  at  right  angles  to  the  plane  of  the  coils,  the 
plane  of  the  scale  will  be  a  parallel  to  the  plane  of  the  coils 
when  the  ends  of  the  scale  are  equidistant  from  the  suspension- 
head. 

Adjust  the  control  magnet  until  tlie  spot  of  light  is  at  the 
zero  of  the  scale. 

The  galvanometer  is  now  ready  to  be  used.  Connect  the 
Lattery,  the  reversing-switch  and  a  large  resistance,  li,  in  series 
as  before.  Unplug  a  large  resistance  from  the  box ;  half  a 
megohm  will  not  be  too  much  to  begin  with.  Close  the  circuit 
and  o])serve  the  dellection.  If  the  detlection  be  small,  reduce 
the  resistance  in  the  circuit  until  about  3<»0  scale  division  is 
<)])tained.  If  the  spot  goes  oflf  the  scale,  increase  the  resistance 
until  a  deflection  of  about  30(»  scale  divisions  is  obtained. 

Revenue  the  current  and  take  the  mean  readiiig  as  6. 

Now  shunt  the  galvanometer  with  a  known  resistance. 

Adjust  the  shunt,  S,  until  a  deflection  of  about  150  is 
obtained. 

Reverse  and  read  again. 


KLKCIinvliY. 


1U7 


The  mean  gives  rf,. 

Calculate  (f  l».v  formula  (1>). 

Shunt  the  galvanometer  again,  S^,  and  adjust  till  ii  de- 
tlectit.n  of  ahout  loO  scale-divisions  is  ohtiiini'd. 

Reverse  and  read  again,  taking  the  mean  reading. 

\\y  means  of  this  reading  and  d,  above  calculate  G  from 
formulii  (12). 

Example.— Enter  results  thus: 


Slue  oi-  Tangent  (iulvuiioiiieter, 


Mean 

R 

s 

DfHtH.'tioi 

6.50 

-.00 

2M.6 

650 

0 

05. 3 

1027 

0 

60.3 

1027 

100 

26.4 

825 

0 

63.8 

825 

100 

27.6 

Mean  G 104.8 


Blanh  to  he  filed  in  hy  ntudent. 


Sine  or  Tangent  Galvanometer. 

Kef     ting  Galvanometer. 

,_ ■ \ 

R 

.s 

Mean 
Defleotion. 

a 

R 

8 

Mesn 
Deflection. 

a 

1 

0   

Me.in 

J/..... . 

iil 


108 


LA  noil  A I  (Hi  Y  pii  rstcs 


6a.    TO    MEASURE    RESISTANCES    BY    MEANS    OF    A 
WHEATSTONE'S  BRIDGE. 

References. — As  in  K.\i)c>riiii(>iit  r>:>. 

Apparatus  Required. — A  Wluut-toiR''!*  hridjjc;  resistance- 
to  l)t'  !iiea«urcd;  a  seiiHitive  ^itlvuiioini-ttr;  srvcral  luittt  i  io  : 
two  oontJict-keys. 

Theory  of  Experiment. — (1)  7't>  Mt'dxnn  t/i,  lirstsfmn, 
in  a  Coll  of  Wire. — The  theory  of  tlie  WiicatKtom''rt  liridj^e  is 
exactly  the  same  as  that  of  the  I?.  A.  bridge,  which  is  oidv 
a  siiiipU'  form  of  AVlieatfitone's  hridj^e  siiitabU'  for  measuriiif; 
small  resistances. 

In  the  Wheatstone's  bridge  the  arran«;ement  is  as  in  ig. 
41. 


In  the  fiiiuio  /*  and  Q  are  fixed  resistances,  R  an  adjnst- 
able  resistance,  and  .s'  an  unknown  resistance. 

When  li  is  adjusted  .so  that  no  deflection  <»f  thi' jralvanom- 
eter  is  obtained  on  dosinj^  A',  and  A', 

/'  _   .V 

p 


or 


S 


Q 


n. 


(2)    To    Midxiivi'    fh(    !,'•  sisfiiiii-i     of  the  (JiiltuiitomeUi' : 


KLKVTUIVITY. 


lt)0 


Thonip»oiCA  iVf/Aorf.— Since  no  current  flows  through  the 
gulvanoineter,  when  the  proiwr  u.ljii?tnient8  for  the  n»ea«»ure- 
ment  .»f  .S"  have  heen  made,  that  in,  when  Cuiul  D  arc  at  the 
same  potential,  tlio  current  Howing  through  each  arni  of  the 
hridge  renmins  unclianged  whether  K  he  cU)se<l  t>r  not. 

Hence,  if  instead  of  S  a  giUvanoineter  were  in  the  arm 
<:ii,  its  deflection  due  to  th  ^  passage  of  the  current  throujjii 
the  hridge  would  remain  unchanged  whetiicr  A'  he  closed  «)r 

not. 

It  follows,  therefore,  that  if  the  galvanometer  he  put  in 
the  arm  Cli,  and  H  he  adjusted,  until  on  closing  CD  directly 
through  A'  no  change  of  deflection  in  the  galvanometer  is 
nhserve*!,  T  and  /)  have  the  same  jM-tcntiul.  For  if  a  cur- 
rent flowed  from  C  to  />,  the  current  flowing  thrt.ugh  the 
galvanometer  would  change,  causing  a  change  of  «letlecuon. 
Hence 

Q     ir 


or 


P 


(3)  To  Measut'ethe  Resistance  of  the  Buttery:  Mance's 
Method.— li  a  hattery  he  placed  in  the  arm  Cli,  a'ld  the  gal- 
vanometer again  hetween  C  and  D,  on  dositig  A'  a  deflec- 
tion  of  the  galvanometer  will  he  produced,  due  to  the  current 
from  this  hattery  flowing  through  the  system. 

It",  therefore,  li  h'"  adjusted  until  no  change  in  this  de- 
flection is  ohserved  on  losing  A',  rand  />  are  at  the  same 
p(jtential  as  far  as  the  hattery  hetween  A  and  Ji  is  concerned. 
Hence 

p  _  n 


or 


P  ^ 
li  =  ^/?. 


where  U  is  the  resistance  of  the  hattery  in  the  arm  CB. 


200 


LA  nun  A  TOR  T  VII YSICS. 


u 

I 

r 

! 


Further,  since  no  current  lions  through  tlie  gulvaiiotneter 
from  the  battery  B,  when  the  proper  adjustuienis  are  nuule, 
it  may  be  removed  altogether  and  AB  connected  directly 
throuffh  A',.  R  can  then  be  adjusted  until  one  losing  h\  no 
change  in  the  galvanometer  detiection  is  observed. 

In  practice  i.  is  convenient  ti  bring  the  galvanometer 
needle  back  to  zero  by  means  of  control  magnets. 

Practical  Directions.— (1)  In  the  ordinary  Wheatstone's 
bridge  the  airaugement  is  as  in  Fig.  42,  the  letters  having 


Fig.  'C. 
the  same  meaning  as  in  Fig.  41,  the  numbers  inJ^.cating  the 
resistance  that  caji   be   unplugged   from  the  bridge  at  the 
points  corresponding  to  the  open  spaces. 

A  sensitive  gal'.anometer  is  required  if  accurate  measure- 
ments are  to  be  made.  A  reflecting  galvanometer  with 
telescope  and  scale  or  lamp  and  scale  is  most  suitable. 

Coi.iplete  the  connections  as  in  Fig.  42,  putting  con- 
tact-kevs  in  both  the  galvanometer  and  battery  circuits. 
Unp.ug  from  both  P  and  C^  loO  ohms.  Shunt  the  galvan- 
ometer with  a  suiall  resistance  while  tlie  trial  observations  are 

being  made. 

Unplug  a  resistance  from  the  arm  li,  and  close  the  battery 
kov  and  galvanometer  key  in  the  order  named. 


ELECIltlCITY. 


201 


Observe  the  direction  of  the  detloctioii  of  the  galvanom- 
eter. 

Change  the  resistance  m  H  until  tlie  deflection  is  in  the 
opposite  direction. 

The  value  of  S  lies  between  these  two  values  of  R. 

Continue  to  adjust  Ji  until  by  changing  it  1  ohm  the 
direction  of  the  reflection  changes  from  left  to  right. 

Now  open  the  shunt  of  the  galvanometer  so  as  to  increase 
its  sensitiveness. 

Change  P  and  Q  to  \Q  and  100  respectively. 

Adjust  li  as  before,  starting  with  10  times  the  resistance 
of  the  smallest  of  the  two  previous  adjustments. 

This  will  give  the  resistance  to  the  first  decimal  place. 

Make  P  10  and  Q  looo,  rei)eating  the  adjustments  for  li. 

This  gives  *V  to  two  decimal  ])lac('s. 

Rei)eat  the  observations  for  the  (»ther  resi.-tanoes. 

(2)  Put  the  galvanometer  in  the  place  of  the  resistance  S. 

Put  a  large  resistance  in  series  with  the  battery  between 
the  points  A  and  />*,  thus  dinuidshing  the  current  flowing 
throusrh  the  system. 

Adjust  this  resistance  until  on  closing  the  battery  circuit 
the  deflection  of  the  galvanometer  is  on  the  scale. 

Kepeat  the  adjustments  for  P  and  Q  as  in  (1),  leaving  the 
galvanometer  circuit  closed. 

Adjust  7?  until  on  closing  CD  directly  through  a  key  no 
chanire  in  the  £falvanometer  deflection  is  observed. 

('alculate  G. 

On  changing  the  values  of  P  and  Q  in  this  case,  a  change 
in  the  galvanometer  deflections  will  also  take  place,  and  the 
resistance  in  series  with  the  battery  may  have  to  be  atljusted 
to  briiig  the  spot  of  light  again  on  the  scale. 

(;'.)  Now  put  the  battery  in  place  of  -S*,  and  the  galvanom- 
eter a:rain  between  C  and  I). 


202 


LAliORA  Tony  i7/)  .S7CV. 


Put  a  contact-key  in  the  circuit  between  .1  and  B. 

By  means  of  n)a^net8  bring  the  spot  of  light  to  the  i«ro 
of  the  Bcale. 

Adjust  li  until  with  /'  equal  to  10  and  Q  equal  to  lOO 
no  deflection  is  obtained  on  closing  the  key  between  A  and  B. 

The  resistance  of  the  battery  is  thus  obtained  to  one 
decimal  place. 

Repeat  the  observations  for  the  othe-  batteries  given. 

Example. — Enter  results  thus : 


Resistance. 


Coil  A 

"    B 

"    C 

Galviinoineter . . . . 
Leclanche  buttery 
Dniiiell  battery. . . 
Dry  cell 


10 
M 
100 
100 
10 
10 
10 


Blank  to  hejilhd  in  hy  student. 


V 

R 

S 

1000 

2575 

35.75 

1000 

3645 

36.45 

1000 

2«94 

29H.4 

1000 

273 

27  3 

100 

14 

1.40 

100 

85 

8.5 

100 

503 

5(1.3 

Rebistance. 

P 

Q 

R 

s 

\      ^aKJai^*? 


Kl.hxrniclTY. 


'xi; 


63.  (I)  TO   VERIFY   JOULE'S   LAW,  JH  =  CTRt. 
(2)  TO   FIND   THE   VALUE   OF   ,/. 

References.— S.  Tliompson,  p.  436;  Knott,  pt.  tt.  p. 
lOO;  IJarker,  p.  70i> ;  Hastings  and  Jieacli,  p.  MO;  Ames, 
p.  2*25);  Nichols  and  Franklin,  vol.  11.  p.  4S ;  AVatson,  p. 
702;    Anthony  and   Urackett,  p.  31!>. 

Apparatus  Required. — Two  copper  voltameters  or  two  gas 
voltameters;  two  calorimeters  with  resistance-coils  and  stir- 
rers ;  two  thermometers. 

Theory  of  Experiment. — (1)  Joule's  Law  may  be  stated 
p  follows:  T^>e  heat  i)roduced  in  a  given  time  in  any  part 
.  a  circuit  is  proportional  to  the  square  of  the  current  and  to 
the  resistance  of  that  particular  part  of  the  circuit. 

The  law  may  also  he  stated  thus:  If  a  current  C  tiow 
through  a  resistance  Ji  for  f  seconds,  the  work  done  in  driving 
the  current  through  the  resistance  is  given  by  the  c(puvtion 


w=  cm". 


(1) 


If  now  the  heat  deveh)ped,  which  meiisuresthe  work  done, 
be  utilized  to  warm  a  mass  of  water  J/  from  a  temperature  t 
to  a  temperature  /,,  we  obtain  the  relation 


ir 


JMit,  -  0, 


(2) 


where  ./"is  the  mechanical  e(|uivalent  of  heat,  that  is,  the  work 
done  in  raising  one  gram  of  water  through  1"  C. 


Hence 


JM{t,  -t)=  C'Rt", 


tidi  LAUOliATOUr  PJITSICS. 

or  denoting  M  (<,  —  t)  by  II, 


(2)  Since 


or 


jii  =  cut' 


JU  =  C'Rt", 


J  = 


cut' 


H 


.     (3) 


(4) 


From  equation  (4)  ^  n  be  calculated  if  the  observations 
for  L\  R,  t"y  and  //be  nsadc. 

Ill  tlie  above  ecjuations  all  the  quantities  are  expressed  in 
C.G.S.  units.  In  making  the  observations,  liowever,  (/and 
R  are  usually  measured  in  practical  units. 

Since  1  ampere  =  ^„  C.Ci.S.  units 

and  1  ohm       =  10'  C.(i.S.  units, 


we  have 


or 


JH  = 


10' 


C^RWt" 
~l0V/    ' 


C^Rt^' 


•      • 


(5) 


the  measurements  being  made  in  practical  units. 

The  current  can  be  measured  by  a  copper  voltameter  (see 

Experiment  52)  by  means  of  equation  C  =  -,  where  6  is  the 

copper  deposited,  e  the  electro-chemical  equivalent,  and  t"  the 
time. 


«  1 


ELECTIUCITY. 


205 


7i  can  he  measured  by  nieuiis  of  a  B.  A.  bridge.  The 
heat  can  be  measured  by  means  of  a  water  calorimeter,  the 
coil  of  wire  being  inunersed  in  it  while  the  current  tlows. 

Practical  Directions. —  To  Vei'!/'/  the  Iaho. — A  convenient 
method  is  to  use  two  calorimeters  and  two  voltameters  con- 
nected iu  series  (see  Fig.  43).     M^  and  J/.iV,  are  two  cop;  i . 


Fid    43. 


voltameters ;  P^and  P,Q,  are  two  calorimeters  with  coils  6'and 
L\  of  different  resistances ;  /•  is  a  resistance  shunting  one  calo- 
rimeter and  one  voltameter  in  order  to  obtain  a  different  heat- 
ing current  in  each  case.  If  the  experiment  be  performed  in 
this  way,  two  observers  are  necessary,  in  which  case  it  will  be 
well  for  one  to  take  charge  of  tlie  shunted  and  the  other  of  the 
unshunted  part  of  the  apparatus.  Each  observer  can  make 
his  own  observations,  cheeking  when  possible  the  observations 
of  the  other. 

The  work  recpiired  of  such  observer  will  then  be  as  fol- 
lows : 

Clean,  dry,  and  weigh  the  plate  of  t..e  voltameter  on  wliich 
the  copper  deposit  is  to  be  made  (see  Experiment  53). 

Denote  the  weight  by  /*. 

Weigh    carefully  the   cop|)er    vessel  of  the  calorimeter, 
denoting  the  weight  \y  W. 


'2()i\ 


LAiwji. I  run  y  rii rsics. 


I*;irtiully  rill  the  vessri  w  itli  watiT  and  wciglj  again,  denot- 
ing tlie  weight  liy    )!', ;  then 


J/ 


ir,  -  w 


where  J/  is  the  mass  <tf  the  water. 

Tile  ••  water  eiitiivalent  "  of  tlie  eHK)rinietiT  is  found  hv 
niuUiplviiig  its  nut.ss  hy  .O'Jo,  tiie  siuritic  lieut  of  copper. 

Tlie  total  mass,  therefore,  to  be  heated  is 

The  water  shoidd  be  reduced  in  temperature  to  about  as 
far  below  the  temperature  of  the  room  as  it  will  be  above 
tliat  temperature  after  heating,  in  order  t<.  compensate  for  the 
lo.ss  of  heat  by  radiation.  If  the  temperature  of  the  room  be 
17'  ('.,  it  will  lie  possible  to  cool  the  water  down  to  about  1(»° 
or  12°  and  then  to  heat  it  to  1>L>"  or  -24°.  In  order  to  get  the 
same  rise  of  temperature  the  coil  of  the  shunted  calorimeter 
should  have  a  greater  resistance  than  the  coil  of  unshunted 
one,  and  the  resistance  of  the  shunt  adjusted  to  give  a  suitable 
current.  The  sliunt  can  l)e  found  by  calculation  if  the  re- 
sistance (»f  the  calorimeter  and  voltameter  lu."  known  apj)roxi- 
mately,  or  better  still  by  making  a  few  trials  and  adjusting  its 
resistance  until  a  rise  of  one  degree  is  obtained  in  each  in 
approximately  the  same  tiwe. 

As  a  source  of  current,  the  lighting  circuit,  if  direct  cur- 
rent, can  be  utcd.  A  couple  of  storage  cells  also  make  a  suitable 
current  supply. 

Be"  .re  turning  on  the  current,  stir  tlie  water  in  the  calo- 
rimeter and  read  the  temperature  t.  This  must  be  done  simul- 
taneously l)y  the  two  observers. 

Turn  on  the  current,  recording  accurately  the  time,  and 
watch  the  rise  of  temperature  in  the  calorimeter,  stirring  every 
few  minutes. 


.1^  \ 


KLKVTIilCITY. 


207 


Tlie  required  rise  of  teini)erature  will  usUiiil}-  he  ohcuiiied 
in  from  ten  U)  twenty  minutes. 

Observe  carefully  the  time  of  turning  otf  the  current. 

Stir  (juickly  reading  the  temperature  when  it  reaches 
its  highe^^t  point.  This  will  not  he  for  some  time  alter  the 
crrent  is  turned  off,  due  to  tlic  heat  in  the  wire. 

Denote  the  temperature  by  t,. 

"Wash,  dry,  and  weigh  carefully  the  i)late  iii  the  voltameter 
on  which  the  copper  was  deposited. 

Denoting  the  weight  by  1\  and  the  difference  by  rf, 

6  =  I\-  1\ 

Measure  the  resistance  of  the  coil  by  a  IJ.  A.  bridge. 

c-       *  -•  ('■'P-  {       ^'       V/.. 
7/=  (/,  -  t)(,M  -\-  .(•{♦;-)  ir). 

Denoting  the  ratio  of  the  //obtained  from  the  shunted 
calorimeter  to  that  obtained  from  the  nnshunted  by  /■,  and 
the  ratio  of  the  G  R  obtained  from  the  sliunted  voltameter  to 
that  obtained  from  the  nnshunted  I)y  /,,  then,  the  law  Ijeing 
true, 

/'  =  /',. 

(2)  By  means  of  the  observations  oi  one  calorimeter  and 
voltameter,  calculate 

e/ 

10'" 

Preci^ations — (1)  If  the  lighting  circuit  be  used,  be  sure  and 
have  a  lamp  in  series  v 'th  the  apparatus.  The  switch  in  the 
lamp  will  then  serve  for  turning  on  and  off  the  current. 

(•J)  l>e  sure  the  negative  pole  of  the  current  snj>p]y  is  con- 
nected to  the  j)late  of  the  voltameter  on  which  the  deposit  is 
to  be  made. 

Ill  Fig.  43,  ^'anii  /f,  are  the  negative  plates. 


208 


LA  liOH.  I  TOIi  Y  ril  YSICS. 


u 


t. 

f 


(.?)  If  tlie  coil  l>e  woinul  on  ii  fruiiic  tliu  water  equivalent 
of  the  part  immersed  should  also  be  obtiuned,  and  tor  great 
accuraev  that  of  the  thermometer  bull)  as  well,  lu  the  ex- 
periment recorded  below  these  connections  are  put  in  under 
the  heading  J/  -f  -^"^^  ^^^- 


VOI/r AM KTEIl  OBSERVATIONS 

• 

M  4H-,' 
,V,).'.'3,5 

.Vl.fi6.5 

i 

t" 

688 
688 

C 

.K)S 

.y,t» 

4:!  rr> 

1 

r 

i.irrs 

Sliiiiiteil  voltaiiii'lt^r 

L'lishiiiileil  TolliimcliT... 

.183 
.•J08 

CALOUIMETEU 

OBSERVATIO>fc 

. 

W 

90.4fi 
8-.'.96 

»•, 

M+.in).'>ir 

t 

8.50 
8.38 

:J6.:5 
ac.13 

// 

4.'i70 
3551 

r, 

l.'.fS 

Sliiintfd  calorlmetfr 

Unshuiitfd  caloririieier.. 

:«J».T.5 

:.Tl.t;5 

aoo.05 

10' 


=  4.-J5. 


Blank's  to  he  filed  in  hy  atmlent. 
VOLTAMETER  OBSERVATIONS. 


Pt 


Sliiiiiled  voltameter 

L'lishiinted  voltameter.. 


t" 

c 

K 

r 

CALORI>f  '.TER   OBSERVATION'S. 

\r    j     ir,     .w^.ooriW 


jSlnin'e  '  (•ali>rinieter. .  . .  ' 
lUnshuiiteii  I'.'ilorimettT..  ] 


t 


n 


J 

10' 


1 1'.  t 
:f  * 

it 
I 


ELiaCTlUVlTY. 


2U9 


64.    COMPARISON   OF   RESISTANCES  BY  CAREY   FOS- 
TER'S METHOD. 

References. — As  in  Experiment  57;  S.  Tiiomp.-un,  p.  420. 

Apparatus  Required. — A  B.  A.  Inidge;  u  low-re.si.stiincc 
giilvuiKJiiieter ;  the  two  resintaiices  to  be  coiiipjinMl ;  two  un- 
known l»iit  nearly  etjual  re.<istanee.s ;  a  tliernionM-tei-  tor  I  akin  j^ 
the  temperature  of  the  eoilti  under  comparison;  a  water-hath 
in  which  to  inimereic  tLem;  mercury-cup  conneetort;;  a 
battery ;  a  reveroing-switcli. 


Pio.  44. 

Theory  of  Experiment. — Let  tlie  connections  first  he  made 
as  in  Fijj:.  44  (n),  where  x  and  ij  are  tlie  resistaiK-cs  to  lie 
compare<l.  A  and  ^  the  "ratio  re-i.-tances, "  which  are  nearly 
equal  to  one  another;  <",' the  position  of  the  slidinir  cotitact 
when  a  balanec  i>  obtained  on  the  bridfro-wire ;  a  and  h  the 
distances  of  C  from  the  ends  of  the  bridge-wire;  I  the  lenjrth 
and  (T  the  resistance  per  centimetre  of  the  wire. 

Let  )'  and  /•,  be  the  resistances  of  the  intervening  copper 
straps. 

Then  we  have 

A  _■''+'■-!-  <^fi 


mi, 


lii 


I- 1 

i  ■  i 


r  S' 


I-  E' 


=  1:1 


210 


LADORA  TOR  Y  PII YSICS 


On  interchanging  x  and  y  as  in  Fig.  44  (?>),  we  have  on 
obtaining  a  balance  again,  where  the  new  position  C,  is  dis- 
tant a,  and  6,  from  the  ends  of  the  bridge. 


Hence,  equating  (1)  and  (2), 

y  +  r,  4-  0-*  —  ^ -f-  /•,  +  0-6,  • 
By  adding  unity  to  eacli  side  of  (3)  we  have 

a- 4-  /•  4-  o-« + y  -f  r,  4-  ffh  _  y  +  »•  +  <^".  +  "'4-^.  +  q'^ 


(2) 


.'/  +  ''.  +  (^^ 


i^  +  '■.  -h  <^*. 


(3) 


,   (4) 


or 


a' 4-  >'  +  y  +  /■■  +  Q-(tt  4-  ^)  _  y  +  ^'  +  -^'  4-  ^'i  +  q-(tf.+  ^O^  /gx 


y  +  i\  +  o-i 


ic  4"  ''i  4"  o"^! 


Hence,  snice  {a  +  h)  -  (a.  4-  J,),  the  numerators  of 
these  fractions  are  equal,  and  therefore 


or 


y  4-  r,  4-  <r&  =  a;  4-  r,  4-  o-J, , 
y  —  x  =  o-(J.  —  5),    . 


(6) 


a  formula  quite  independent  of  the  resistances  A  and  B, 
and  iilso  of  the  other  resistances,  r,  /', ,  which  enter  as  errors 
into  the  ordinary  B.  A .  bridge  methods. 

It  is  therefore  clear  that  this  is  a  very  convenient  and 
accurate  way  of  comparing  small  resistances. 

To  obtain  the  greatest  accuracy  by  this  method,  it  is 
essential  that  the  resistances  A  and  B  should  not  differ  much 

from  ,r  and  //. 

In  using  formula  (fi)  it  is  of  course  es  .itial  to  know  <r, 
the  resistance  per  linear  unit  of  the  bridge-wire. 


KLEClUIcn'Y. 


211 


\ 


I 


Tho  value  of  rr  may  l»i'  easily  (k'ti-nnincd.  A  fiiinpio 
iiH'tlnMJ  is  to  tlrtiTinim;  tlit-  ilifTfiTiiiv  lietweeu  a  known 
stuiuliinl  rcsistanci"  /'  and  a  ne';li<jil)ki  re8istancc  Q.  In 
which  case,  from  formula  (<)j,  wc  have 

or,  since  ^  =  0,  we  liavo 

a  = 


",  -  «, 


(7) 


where  <?,,  rt,  are  again  tho  distances  of  the  balance-points  from 
one  end  of  the  bridge. 

A  simpler  but  less  accurate  method  is  to  measure  the 
resistance  oi  the  whole  bridge-wire  /  by  means  of  another 
li.  A.  bridge,  and  divide  the  resistance  by  the  length  /  of  tho 
bridge -wire. 

Or  again  suppose  that  instead  of  x  and  y  two  statulard 
one-ohm  coils  be  i»ut  in  the  bridge  and  shunft-il  siu-cessively 
with  a  standard  lO-ohm  coil  and  the  system  balanced  in  each 
case.  Then,  tho  difference  of  the  resistances  in  this  case 
being  j\  ohms, 

where  _/  and  j,  are  the  distances  from  one  eiul  of  the  bridge- 
wire  of  the  balance-points  in  the  two  adjustments. 


Hence 


1 


or 


<T  =    i-i^T 


ii(i-i.)* 


This  is  a  .-iiiiple  and  accurate  method  of  measuring  rr. 

Practical  Directions. —  To  Compare  x  and  //. — Make  con- 
nections as  shown  in   Fig.  44  {a),  I{  l)eing  a  reversing-key. 


I 


212 


lahoua run r  rii rsics. 


I 


Tho  Ci)iU  Hhould   Ih5  coimucted   in   tlio  Idulge  by  meuns  of 
mercury  cujw. 

Sou  that  tho  terinimils  of  ull  tlic  coils  aro  well  tJt)wn  on 
the  hottoiim  of  the  imrciiry  cups. 

A<lju.-t  ♦'     hlidiiig  contiut  until  a  halunco  irt  ol»tuiiie<l. 

Ucvertic  tiic  huttcry  current  and  liulance  again  to  eliuiinato 
any  error  due  to  thcniial  eirects. 

Take  the  mean  t)f  the  two  readiii;;s  for  tlie  position  of  ('. 

Interchanire  u-  mkI  y,  Fig.  4+  (A),  and  proceed  as  l»efore, 
obtaining  a  mean  value  for  the  position  of  (\. 

Then  j-  —  y  =  (Tyf\  —  h),  where  A,  —  i  is  the  length  from 
6'to  (\. 

To  Jhirnii'nn'  rr. — I'ko  a  standard  resistance  eomewhat 
Binaller  than  that  of  the  bridge-wire,  and  also  a  tldck  eojjper 
strap,  the  resistance  of  wliich  can  be  neglected,  in  place  of  x 
and  V.  snid  rej-oat  the  observatioiiH  m  above,  reversing  the 
current  ami  taking  a  mean  reading  in  each  c;isc. 

Denote  the  distances  of  C  and  ^',  from  the  zero  end  of  the 
bridge  by  »?,  and  d^. 

Either  of  the  other  methods  mentioned  on  page  211  will 
do  equally  well. 

Calculate  the  value  of  <r  from  formula  (7),  and  the  value 
of  X  —  //  from  (0). 

Tf  either  x  or  //  be  known  absolutely,  the  other  will  be 
completely  deternnned. 

If  one  of  the  resistances  be  a  (Jerman-silver  standard  or 
other  ordinary  standard,  it  will  be  necessary  to  take  its  tem- 
])erat)irc  in  a  water-bath,  and  correct  for  it.  The  tempera- 
ture cannot,  perhaps,  be  known  closer  than  ^'„°  on  account  of 
the  very  thick  coating  of  paraffin  and  silk  around  the  re- 
sistance, but  the  error  duo  to  that  discrepancy  would  be 
trifling.  If  the  standard  be  of  resistance  li  and  correct  at  a 
temperature  f,  and  the  observations  i>e  made  at  a  temperature 


^i  } 


liiiit 


KLECTRICITY. 


213 


/, ,  then  the  true  resiHtance,  /;, ,  of  gtiuulurd  at  teinperature  t^ 
U  given  b}'  ecjuutioii 

//.  =  //!!  +  «(/. -OS, 

a  being  the  temperature  coetticieiit  of  tlie  wire. 

All  the  bridge  reiulingd  should  be  taken  to  ^^  of  u 
niilliuietre. 

Use  for  jc  a  btandanl  one-ohm  coil  and  caleulute  //. 

Precautions. — It  is  neeessury  that  the  termiiiuls  of  the 
coils  should  make  a  good  steady  eontuct  with  the  bridge. 
They  should  therefore  be  well  amalgiimated,  and  if  necessary 
tied  down  to  the  l)ottom  of  the  cups  with  rublter  bands. 

The  battery  current  must  always  be  reversetl  at  each  bal- 
ance-point, in  v.rder  to  eliminate  the  etlVct  of  thcrmo-currents. 

If  a  storage  battery  is  used  for  tl»e  source  of  current,  be 
careful  not  to  short-circuit  it. 

Example. — Knter  results  thus : 


/• 

<  iliservalioiis  fur  a. 

a 

.0055") 

62.5 

OI)servfl 

llon,«  for  jr  --  ;/. 

Mean 

Mean 
"1 

'       1      'i 

o(/.,-6) 

.1 

57.5 

39.5 

39.1 

10.4      17.0 

.013 

Ithnd-  to  h  fll'J  hi  hy  student. 


Observations  foi  a. 


Mean         J  ■  ean 


Observations  fur  x  —  y. 


ail)  I-  b) 


214 


LABORATORY  PHYSICS. 


65.  TO  CALIBRATE  THE  SLIDE-WIRE  OF  A  B.  A.  BRIDGE 
BY  CAREY  FOSTER'S  METHOD. 

References. — As  in  Exporiiuout  Oi. 

Apparatus  Required. — The  IJ.  A.  bridge  wliicli  is  to  l»e 
calibrated ;  a  snpplementtiry  bridge-wire  having  a  sliding 
contact,  or  a  second  13.  A.  bridge;  a  small  resistance  having  a 
value  equal  to  about  one-tentii  the  resistance  of  the  whole 
bridge-wire;  a  stout  copp^r  strap  of  negligible  resistance; 
two  pairs  of  mercury  cups;  a  reversing-switch ;  an  ordinary 
contact-key;  a  battery;  a  suitable  low-resistance  gananoiu- 
eter. 

Theory  of  Experiment. — In  the  previous  exjjerinient  it 
was  assumed  that  the  resistance  of  a  unit  length  of  the 
bridge- wire  was  uuiform  thioughout. 


A, 


e^ 


B 


Fio.  45. 


^ 


m% 


i 


f.S 


The  object  of  the  present  experiment  is  to  test  the  uni- 
formity of  the  wire  by  determining  tlie  resistances  of  oipial 
portions  of  the  wire  at  different  ])ositions  along  its  leuL'th. 

Let  the  two  bridge-wires  ^i?  and  ^,i?,,  with  the  small 
coil  and  copper  strap,  be  connected  as  shown  in  Fig.  4.5,  the 
sliding-c  act  P  being  as  close  as  possible  to  /?,  the  other 
slidnig-(  uact,  P, ,  being  adjusted  until  no  galvaiiometer  de- 
flection .  (>'  led.  Then,  denoting  tlie  resistance  of  AB 
by  I,  of  A,ii,  by  I,,  of  the  small  coil  (called  the  "yflfJ/ye") 
by  G,  of  the  copper  strap  (called  the  ^^  connector'''')  by  C, 


'V-\\ 


ELECTRICITY. 


215 


and  the  resistances  of  the  connecting  wires  by  e,  e,,f,f,,  as 
shown  in  Fig.  45,  we  have,  froni  the  theory  of  the  B.  A. 
bridge,  the  following  relation  : 


(1) 


r,  being  the  resistance  i.f  the  length  AJ\  of  the  wire  A,B,. 
It  C  and  G  be  now  interchanjred  and  /*  moved  along  the 
AD  until  a  new  balance-point  is  obtained,  we  obtain  the 


wire 
eciuation 


r: 


.     (2) 


where  ris  the  resistance  of  the  portion  of  the  wire  between  A 
and  the  new  position  of  P. 

E(iuating  (1)  and  (2),  adding  unity  to  each  side  and  in- 
verting, we  obtain 


Hence 


(?4./=C-f/  +  ^-^, 


or 


G-  C=l-r; 


(3) 


that  is,  the  resistance  of  the  length  I  -  r  through  which  the 
slider  was  moved  to  obtain  a  balance  is  equal  to  the  difference 
in  resistance  between  the  connector  and  gauge. 

If  now  P  be  left  at  rest  and  P,  moved  until  a  balance  is 
again  obtained,  it  will  be  found  that  the  length  of  wire  over 


'^  WfFWWm^i^- 


r^:l! 


21G 


lAUOUATOHY  rilYSICS. 


wliich  P.  is  moved  is  ecjual  to  the  difference  between  the  c(jn- 
neotor  uiul  jjau-e.     Hence  both  wires  are  calibrated  simnl- 
taneuuslv,  since   lengths  on   both  wires  of  e,,nal   resistance 
Iiavni-  a  value  equal  to  the  dillerence  between  the  gauge  an.'l 
connector,  arc  obtained. 

•  The  i-esistance  of  the  gauge  niaj  be  measured  as  in 
the  last  experiment,  using  the  connector  as  the  negligible 
resistance. 

The  value  cf  a  for  each  length  is  obtained  by  dividin.^ 
the  value  of  G  -  C  by  the  length.  * 

Practical  Directions.-^Like  connections  as  in   Fi.^    45 
puttmg  a  reversing-switch  in  the  batterv  circuit. 

The  connector,  C,  at.d  gauge,  G,  should  be  connected  in 
by  means  of  niercury  cuj.s,  the  contact-].oints  being  well 
amalgamated. 

With  the  connector  and  gauge  as  figured,  set  7'  close  to  B 
and  balance  by  moving  P,.  Reverse  the  battery  current  and 
balance  again. 

The  mean  reading  gives  the  length  corresponding  to  the 
resistance  I,  -  r.,  the  first  calibrated  length  on  A,  L\  if  F  be 
at  the  extreme  end  of  AB. 

Interchange  C  and  G,  and,  keej)ing  I\  fixed,  move  P 
until  a  balance  is  obtained.  Reverse  the  batteiy  current  as 
before  and  balance  ajrain. 

The  mean  reading  gives  the  lengtli  corresponding  to  Z  -  r, 
the  first  calibrated  length  on  AB. 

_  Again  interchange  C  and  G,  and  move  >,  until  a  balance 
IS  obtamed,  repeating  the  adjustments  and  observation  along 
the  wire  alternately  until  the  end  of  one  of  them  is  reached. 

Determine  G  -  C  by  one  of  the  methods  indicated  in  tlie 
last  experiment  and  calculate  the  value  of  a  for  each  of  the 
lengths  I  —  r. 


iMpm 


•".•«.V'Vj^"1[' 


.-^V.A    K  ftJ..J 


i*S_ 


:jwm  '^mm^m-f^m 


•■'••■  Vyi-  •'•■  ^r-  - 


ELECTRICITY. 


217 


Example. — Enter  results  thus ; 

0-  (7  =.053. 


ReaUinK 
Bri<li?e  AH. 

Difference. 

a 

Br!?r;e';r«,'  ^'«"--- 

i 

0 
9.56 

.00554 

8.75 
IT  44 

1 

9.56 

8.69 

.00610 

19.16 

9.60 

•0055'i 

26.04 

8.60 

.00616 

28.73 

9.57 

.00554 

34.79 

8.75 

.00605 

38.36 

9.63 

.00550     j 

43.46 

8.67 

.00611 

47.96 

9.60 

.(M)552     ! 

53.19 

8.73 

.00607 

57.51 

9.55 

.00555     j 

60.83 

8.64 

.00613 

67.09 

9.58 

.00553     I 

69.48 

8.65 

.00613 

76.63 

9.54 

.00555 

78.18 

8.70 

.00609 

87.27 

9.64 

.00549 

86.88 

8.70 

.00609 

96.77 

9.60 

.00553 

95.53 

8.65 

.00613 

Mean  value  of  a 

.00552 

Mean  value  of  or. 

.00610 

Blank  to  "be  filled  in  hy  student. 


Reading 
Bridge  AB. 

Dlffereufe. 

a 

ReaiJinjT 
Bii.lKe.4,ft,. 

Difference. 

"' 

Mean  value  of  a 

Mean  value  of  tTj 

218 


LAUGH  A  Ton  Y  PHTBIC8. 


Jfi 


66.  VARIATION  OF  RESISTANCE  WITH  TEMPERATURE. 
TO  DETERMINE  THE  TEMPERATURE  COEFFI- 
CIENT OF  A  CONDUCTOR. 

References.— S.  Thompson,  p.  403;  Nichols  and  Frankh'n, 
vol.  II.  p.  o(»;  Knott,  pt.  II.  p.  199;  Watt^on,  p.  090;  liarker, 
p.  7U;  Carliart,  pt.  ii.  p.  270;  Anthony  and  JJrackett,  ]>. 
319;  Hastings  atul  Beach,  p.  425. 

Apparatus  Required — A  Wlieatstone  l>ridge,  preferably 
one  of  the  dial  pattern ;  a  sensitive  low-resistance  galvanom- 
eter; a  couple  of  cells;  a  hypsometer;  a  vessel  containing  ice 
or  snow  saturated  with  water;  some  mica;  a  metre  of  line- 
drawn  wire  (platinum  .000  in.  is  suitable);  a  reversing-key ; 
a  contact- key  for  making  a  permanent  contact. 

Theory  of  Experiment.— For  small  changes  of  tempera- 
ture the  increase  of  resistance  of  pure  metals  is  found  to  be 
nearly  proportional  to  the  incTease  of  temperature.  If  Ji^  be 
the  resistance  of  a  coil  of  wire  at  temperature  0  ('.,  and  Ii 
its  resistance  at  temperature  t,  then 


R,  =  ^.(1  +  at),      .      .      . 
where  a  is  the  temperature  coefficient  of  the  wire. 


Hence 


liJ 


(1) 


(2) 


If  t  be  100*,  the  boiling-point  of  water,  (2)  becomes 


a  = 


_  ^.00     -    A 


loo  .  7?. 


...     (3) 


If  B,^  and  Ji^  he  measured,  a  can  be  calculated. 
Practical  Directions — 'J'ake  about  a  metre  of   .000  in. 
platinum  wire  and  anneal  it  by  passing  it  slowly  through  a 


I   i. 


i_i    ..J&*ir7^J 


m!k^mi^iw^i^A^..jm 


r.n:. 


:  yr  w? 


ELECTRICITT. 


219 


buiisen  flame.  If  wire  other  tlian  platinum  be  used,  the 
method  of  treatment  will  depend  on  tlie  material.  Sokhr  to 
each  end  of  the  plafinum  wire  a  piece  <jt'  Xo.  2o  ccpjier  wire 
about  H  metres  in  length. 

Take  a  strip  of  mica  about  h  centimetres  in  len<r*^h  and  1 
centimetre  wi<le  and  notch  it  with  file-cuts  about  a  millimetre 
ajjart.  On  this  wind  the  i)latinum  wire,  making  a  coil  as  in 
Fig.  46. 


A 

A, 

K        K^ 

WVTAV 

c 

c. 

} 

,1  J          .1 1,--'^ 

B 

B,!"^      ^... 

Fm.  46. 

The  two  copper  wires,  marked  AA^^  ^^n  should  be 
fastened  to  the  mica  by  small  loops  of  wire  passing  through 
the  mica  at  points  corresponding  to  those  marked  K.  This 
should  be  done  before  the  coil  is  wound. 

Now  take  a  piece  of  copper  wire  of  the  s.  me  size  and  equal 
in  length  to  the  other  two  and,  bending  it  at  its  middle  point, 
fasten  it  to  the  mica  in  position  corresponding  to  LX\. 

Insert  tlie  coil  into  a  glass  tube  about  40  centimetres  in 
length  and  just  large  enough  to  receive  it. 

Fit  a  cork  tiglitly  in  the  tube,  allowing  the  coi)per  wires  to 
come  out  by  means  of  notches  in  the  cork. 

If  the  wires  be  double-covered,  they  may  now  be  bound 
together  in  several  places  along  their  length  so  as  to  make  the 
whole  comparatively  rigid,  care  being  taken  to  mark  the  ends 
of  the  leads  connected  with  the  coil. 

The  coil  is  now  ready  for  use. 

The  wires  AA^^  BB^  serve  to  connect  the  coil  into  the 
bridge,  while  CC^  compensates  for  their  resistance  when  con- 
nected into  the  opposite  arm. 


'm 


rr^^^^^^^j^r^pgy^ 


220 


LA liORA TORY  PII YSWS. 


:<Mf 


Connect  the  coil  and  compensating  leads  as  in  Fig.  47, 
31  being  an  additional  insulated  terminal,  hy  means  of  wliich 
the  coil  and  compensating  lead  are  ])ut  into  different  arms  of 
the  bridge,  /-'  and  Q  the  ratio  arms,  i?  the  adjustable  arm 
with  the  com])eu8ating  leads  O,  and  -S*  the  coil. 


Fig.  47. 

Immerse  the  tube  containing  the  coil  to  about  half  its 
length  in  the  vessel  containing  the  snow  or  ice.  Making  P 
and  Q  10  and  10,000  respectively,  adjust  B  until  no  deflec- 
tion is  obtained,  and  continue  to  adjust  7?  until  the  resistance 
of  the  coil  hecomes  steady.  Tiiis  u.sually  takes  about  o 
minutes.  The  resistance  oi  a  coil  of  the  size  mentioned  above 
is  about  4  to  .-)  olnns,  so  tliat  I?  will  be  about  4000  ohms. 

Now  insert  the  tube  into  the  hypsometer,  keeping  its  end 
two  or  three  inches  above  tlie  water,  and  lot  the  steam  flow 
around  it  freely  until  a  steady  temperature,  as  indicated  by 
the  resistance,  is  obtained. 

Read  the  barometer  and  find  the  temperature  of  steam 
corresponding  to  the  barometric  ])re8sure. 

Calculate  a. 

Precautions — The  battery  circuit  should  connect  the 
junction  of  the  two  large  resistances,  ^and  J2,  to  the  junctions 
of  the  two  small  ones,  Pand  -8',  as  in  Fig.  47,  in  order  to  keep 
the  current  flowing  through  the  system  very  small ;  otherwise 
the  coil  will  become  heated  by  it. 


ELKClliltJIIY. 


221 


Tliernio-clectric  effects  ean  l>e  eliminated  by  using  a  ro- 
versing-key. 

llepeat  the  observations  several  times. 
Example. — Enter  results  thus: 


Ice  .. 
Steam . . 
Ice  ... 
Steam . 

Ice 

Steam . . 


V 

R 

s 

« 

t 

I 

a 

10000 

4226. 
5665. 

4.22f) 
5.665 

75. :« 

99.75 

.00341 

4227. 

4.227 

It 

<l 

.00341 

5665. 

5.665 

4226. 

4.226 

.00341 

5665. 

5.665 

1 

1 

Bla^ih  to  he  filed  in  ly  stxdnt. 


K 


H 


5.^ 


67.  TO  MEASURE  A  VERY  SMALL  RESISTANCE. 

"References  as  in  Experiment  56. 

Apparatus  Required.— A  standard  .01  ohm;  a  small  re- 
sistance to  he  measured;  a  storajre-hattery ;  a  plusr  contact- 
kev;  two  Pohl  commutators;  a  sensitive  p^alvanometer. 

Theory  of  Experiment— The  methods  described  in  the 
previous  experiments  are  not  suitable  for  the  measurement  of 


i|r 


^„    If 


.m^' 


oo.» 


LA  BOliA  Ton  r  PJirsiCS. 


very  lar-e  or  vory  B.nall  ri'si  tanc-os.  The  urosent  is  <,no  of 
several  inotl.o.ls  whieh  nnVl.t  he  used  to  detennii.e  the  resist- 
anee  of  a  eoiuhictor  whose  resistance  is  very  small. 

Let  u  stan.lanl  resistance  A>  a.ici  the  nnk.mun  resistance 
A  he  connected  in  series  witli  a  hattery  Ji,  Fig.  43.     Then 


bv  Ohnrs  law,  the  potential  hetvveen  the  j>oints  .Vand  J/  is  to 
tliat  between  A  and  B  in  the  ratio  of  the  resistance  It  to  A',  or 


V. 


R 


(1) 


poll  r/"V^'"rr''  ^"*"'^^*'  -'-^^^^"^^  ^^^--»  the 

pumts  J/and   y  and  the  points  A  and  Zf  respectively. 

1^  now  JAV  and  AB  be  connected  snccessively  to  ter- 
"Hl.  of  a  .aIvanon.eter,  the  deflections  of  the  galvanometer 
III  also  be  proportional  to  the  potential  differences  between 
tile  points. 

Hence,  if  6  and  rf.  be  the  deflections, 


6' 


or 


X=^J,. 


(2) 


4 


irifWitiiinifiiiamiw 


KLKCTIW'ITY. 


223 


It  is  Ufiually  necessary,  however,  to  have  iin  adjustable 
reeistajiee  in  the  galvanometer  eircnit  which  can  l»e  adjusted 
so  as  to  give  aii|)ro.\imatelj  equal  deHections. 

If  S  be  the  resistance  in  series  with  the  galvanometer 
when  its  tenninals  are  connected  to  M  and  -V,  and  *V,  when 
tiiey  are  connected  to  -^1  and  B ;   then 


and 


H 


ence 


6. 


V 


or 


K  __  ^,('S  -f  G) 
V 


or,  substituting  from  (1)  and  solving  for  A',, 


-^.  -  ,s  +  G^  6      • 


(3) 


If  G  be  not  known,  it  can  be  found  by  the  method  de- 
scribed in  Kxperiment  61. 

Practical  Directions.— Connect  in  series  a  storage-batter v, 
the  standard  resistance,  the  unknown  resistance,  and  an  adjust- 
able resistanci',  /•  (a  metre  or  so  of  bare  German-silver  wire 
Xo.  20  is  usually  suitable). 

Ucniove  from  one  of  the  Pohl  C(»mmutators,  P.  the  thick 
wires  (jii  the  base  connecting  the  mercury-cups. 

Connect  (see  Fig.  4  *<)  tie  terminals  of  the  two  resistances. 
It  and  A',  to  tlie  two  pair-  "f  terminals  frotn  which  the  con- 
nections have  bee'i  removed,  and  the  remaininji  nair  of  ter- 


224 


i.AiwRA  Tojir  pursics. 


n.inals,  in  which  the  rocker  <lip«,  to  the  cor  responding  pair 
ot  the  second  coniinutator,  Q.  '  fo  t 

Connect  the  galvanometer  tenninals  to  a  n-maining  pair 
i>t  tLTininals  of  the  second  coninnitat,  r. 

iiy  '-ocking  the  tirst  switch  A /i  an.l  J/.V  ,-an  l.e  succes- 
sively conne,-te,l  to  the  ga!van..n.eter,  and  hv  ro,.kin..  fh. 
second  the  current  can  l,e  reverse<l  in  the  galvanon.cter  circuit 

A  siMfuI.!.  unknown  rc.i.ta.icc  can  he  made  from  a  ,.iece 
of  thick  copper  wire  stretched  hctween  two  ternu-naN 

Halt  a  metre  of  So.  lu  wire  gives  a  snitahle  sn.all  re- 
fiistance . 

Uock  the  switch  to  which  the  resistances  are  attached  so 
^Imt  the  potentml  from  It  is  on  the  galvano.neter  terminals. 
A.ljust  ^  until  a  .suitahle  dcHection  is  obtained 
Keverse  the  current  and  take  the  n-ean  readin<^ 
Kcpeat  the  observations  for  A',  taking  a  n.ean^dctlection. 
Kcpeat  the  whole  series  of  observations  several  times. 
iMeasure  O'  hy  method  of  Kxperiment  61. 
Example — Enter  results  thus: 


.01 


s. 


10000  250 


200      I      2050 


Mean  value  of  j- 


.00130 


Biank  to  heJiUed  in  ly  student. 


». 


Mt'aii  value  of  .r. 


M        II  ■  I  III    "1      II    llIP    %\\\ 


"^^  ■*j..--*-ji.-T_T^a^«-- -■>■.■«:-:     n-^ir;.*.p.:3Mr=ii:3.1 


'iS}%2l^j^^WW^^ 


: 


KLhVTh'icrrr. 


68.  TO  MEASURE   A   VERY   LARGE   RESISTANCE. 

References.  —As  in  K\|HriiiK'iif  .'iti. 

Apparatus  Required. —A  sensitive  liiifh-rcsistaiice  ;;iilvan- 
oineter:  u  miniher  of  cells;  a  int'j.'<.lim ;  a  r.'sistancc-l.ox  lor 
slmiiting  the  galvanometer;  a  reversing-switch ;  resistances  t.. 
I»e  ineasnred. 

Theory  of  Experiment — As  stated  in  the  last  experiment 
tiie  t»niinary  bridge  methods  are  not  suitable  for  the  measure- 
ment  of  very  large  resistances.  The  method  liere  described 
is  a  very  simple  and  direct  one.  similar  to  that  of  ICxperiment 
50,  oidy  large  resistances  and  a  sensitive  galvanometer  are  used. 

Let  a  galvanometer  (r\  a  large  unknown  resistance  A',  and 
a  battery  /i  be  connected  in  -eries  with  the  galvanometer. 
Let  the  K.M.V.  of  the  battery  used  be  /'/,  the  detlection  ob- 
tained d,  and  the  current  through  the  galvanometer  C. 


Tl 


leii 


C 


K 


X  +  li  +  (^ 


-,  -  h'd. 


(1) 


Now  let  the  resistance  X  be  replaced  by  a   known   resi.-t- 
ance  //,  giving  a  detlection  (J,;   then 


Hence 


E 

^'  "  ^  + //+  v;  =  ^'''^■• 
n  j^  n  +  (;  _^ 


(-') 


or,  neglecting  B, 


.r  +  a  ~  6, 


(■') 


If,  however,  X  he  a  very  large  resi>tjiuce,  say  a  number  of 


r 


7^  >ri^::'^ 


mA 


ri  y,.;->:^."r^^ 


i« 


fi    i 


226 


I.AmtRMORY  viiYsns. 


megolmiK,  uihI  R  «me  mep^lim,  it  wll  l^e  iic<-csHary  to  sliunt 
the  jralvHiioiuettM-  when  li  if»  in  the  ( iroiiit. 

If  .Vbe  the  resihtaiice  of  the  «himt,  (2)  hecomeH 


^'1  -  ^x     '"  ^'  4- 


/> 


or 


(/if  4-  /^X^' +  '*^')  +  ^''"^ 

Coinl.iiiiiii,'  (I)  and  (4),  we  obtain 

(/;_+  .s')(/.?  +  It)  +  ^'■'''^' 


.  =  A'<y.. ...    (4) 


rf. 


•       ■ 


.     (5) 


I  )enotinp  ^    by  /•,  neglecting   /?,  and  solving  for  X,  we 


obtain 


A'((;  +  -*^')  ,   (J 


.     (6) 


If  the  galvanometer  bo  provided  with  a  shunt-box,  then 
the  ratio  -'  "^  '""  is  known  and  is  usually  10,  100,  or  1000; 
^1(1  _  ,.)  is  irenerally  small  as  compared  with  7?  and  may 
be  neglectC'l. 

Hence  *v  =  ,^^ 


(7) 


m 


a  eimplo  furrouia  for  ru'K'uiaiiou, 


Fl.f.cTHIill  y. 


If,  licwrvcr.  an  ii<l jii>tiil.lt'  itm  tfiTicr  !«•  used  to  >\\\\\\i  tlic 
giilvaiiKiiu'tt'r,  >'  can  he  adjusteil  until 

(V  =  rf,     or     /'  =  1,1 


a  I 


id  lience  etjuation  (•'»)  ltc«'<'iiies 


(«) 


al^o  a  siiiiplo  foniiiila  for  calculation. 

Practical    Directions.— A   vcn    Miisitivc  jjalvanoinetcr   is 
nece»arv  foi-  this  cxpcritnciit. 

(1)  Mcasniv  the  resistance  of  a  <ieei>  line  drawn  hy  a  h-ad- 
jiencii  on  a  ^-trip  of  white  iiapor. 

[•!)  Meii>ure  tlie  in.-nlation  of  a  coil  of  eotton-covered  twin- 
wire. 

(3)  Measure  the  insulation  of  a  coil  of  ruhher-covered  wire. 

In  tlie  tir.-t  case  the  -trip  of  paper  can  he  «'onnected  into 
tlie  circuit  h_v  means  of  terminals  screwed  into  a  piece  of  hoard, 
the  pai>er  heinir  stretched  on  the  surface  of  the  hoard.  Con- 
!iect  in  a  snfMcirnt  nnndx-r  of  hntterics  to  ohtain  a  detlection 
of  al)out  'JOO  scale-divisions. 

The  reversini;- switch  should  he  in  the  circuit  so  that  the 
current  <-an  he  reversed  and  the  mean  readin<r  taken. 

Suhstitute  a  meirolim  for  the  unknown  resiptance.  and 
shunt  tlie  iralvanonieter  to  ohtain  a  suitahle  detiection  or  the 
same  detlection.  accanliuf,^  as  (7)  or  (S)  is  to  he  used  in  the 

Cidculation. 

In  the  second  case,  separate  the  twin-wires  at  one  end  and 
connect  the  two  wires  at  the  other  end  in  series  with  the  iral- 
vanonieter and  hattery. 

RejK'at  the  observations  and  ei.lculations  as  above. 

In  the  third  case,  place  the  coil  of  wire  iu  a  metal  ve.<r(  ■ 


Jl;^^^^  V^WSk 


228 


LABORATORY  PHYSICS. 


containing  enough  water  to  just  cover  it,  keeping  about  one 
foot  of  the  covered  wire  at  each  end  above  the  surface  of  tlie 

water. 

Connect  in  series  with  tlie  galvanometer  and  battery  one 
end  of  the  wire  and  tiie  edge  of  the  metal  dish. 

Tlie  resistance  thus  measured  is  the  resistance  of  the  wliole 

insulations. 

If  the  rubber-covered  wire  be  soaked  in  water  several 
hours  before  the  trial,  so  '.liueh  the  better. 

In  l)oth  the  second  and  third  cases  the  galvanometer  should 
be  shunted  with  a  large  shunt  fur  trial  observations  to  avoid 
sending  large  currents  through  it   in  case  of  a  very  faulty 

insulation. 

The  wires  connecting  tlie  galvanometer  to  the  unknown  re- 
sistance should  in  each  case  be  carefully  insulated  from  the 
other  wires  of  the  circuit,  and  the  current  closed  by  means  of 
a  tapping  contact- key. 

Example. — Enter  results  thus: 


X 

R 

a           „         "r           ' 

Resistance 
of  x. 

I'encil  mark 

Twin-wire 

Hubber-covered 
wire 

Ml 

5500 

ii 

no 

180 

51 
31 

200 
330 

51  ii 
31  •' 

Infinity 

Bhtnk  to  le  filled  in  hy  stndenl. 


1 

X                    R 

a 

„       1      G  +  .S 

i 

Pencil  mark.... 

Twin-wire 

Kubber-covtred 
wire 

' 

Resistance 
of*. 


^SKaC^"^  I^^^Li '^  /^T^" 


n   Ml   U  I'mHil      i|  I  m 


h'LEcnucn  r. 


•>•){) 


69.    COMPARISON    OF    ELECTROMOTIVE    FORCES    OF 
BATTERIES,  BY  TANGENT  GALVANOMETER. 

Refereni'^s. — Authouy  and  Brackett,  pp.  317,  334-340, 
and  309;  Knott,  pt.  11.  pp.  159-166  and  185;  Barker,  p[). 
561,  699,  and  758,  759;  Nichols  and  Franklin,  vol.  11.  pp. 
54  and  79-85;  Hastings  and  Beach,  pp.  390-395;  S. 
Thompson,  pp.  154  and  163-174;  Carhart,  pt.  11.  pp.  233— 
253  and  273;  Ames,  pp.  233,  306,  and  310-316;  Watson, 
pp.  674,  688,  and  815-823. 

Apparatus  Required. — A  sine  or  tangent  galvanometer ;  a 
resistance- box;  a  contact-key;  batteries  to  be  compared. 

Theory  of  Experiment. — If  a  current  from  a  battery  flow 
through  a  resistance  Ji,  a  galvaiionjoter  of  resistance  6r,  then, 
if  a  tangent  galvanometer  l>e  used, 

,=  A  tan  ^, 


('  = 


B+  (r  -{-  jr 


li  being  the  resistance  and   A' the  E.M.F.   of  the  battery, 
and  B  the  deflection  of  tlie  iriilviiiiometer. 


Hence  E  =  A\B  +  G  +  12)  tan  0. 


0) 


If  now  another  battery  be  used,  E.^l.F.  E^ ,  resistance  B„ 
and  an  external  resistance  /i*, ,  producing  a  deflection  B, ,  then 


E,  =  K{B,  +  <r  +  li     *an  6,. 

E  _  (B  -f  ^'  -4-  7?)  tanff 
Hence         :ft;  -  (^_  +  ^,-  +  7?.)  tan  ^. ' 

or  if  a  sine  galvanometer  be  used, 

/;  _  (/;  4-  G  +  B )  smj 

E-  {B,-f~*r+By^uie: 


(2) 
(3) 


:iyu 


LAJiOHATOUY  rUYOHJH. 


I 


If  the  resistance  of  the  batteries  and  the  galvanometer  l)e 
known,  tlie  ratio,  K/K, ,  can  be  found  at  once. 

If  the  l)attery  and  galvanometer  resistance  be  not  known, 
they  must  first  be  calculated  by  the  metliod  used  in  measuriin.: 
the  resistance  uf  a  galvanometer  and  battery  in  Experinn'nt  :>'' 

Practical  Directions. — Connect  a  Daniell  cell  in  si  rit'>  \> 
a  resistance  box,  the  galvanometer  and  a  reversing-key. 

Unplug  from  the  box  a  hirge  resistance. 

Close  the  circuit  by  means  of  the  contact-key. 

Adjust  the  resistance  E  till  a  suitable  detlection  is  obtained 
say  about  60°. 

Read  the  deflection ,  d. 

Reverse  the  current  and  read  the  defiection  again,  d,. 


e  = 


<5  +'?. 


Auain  adjust  the  resistance  until  tlie  defiection  obtained  be 
about  ;5<»°,  denoting  the  new  resistance  by  Ii,. 
Reverse  the  current  and  read  as  before,  rf, ,  <y,. 


^.  = 


(J, +  <y. 


Then 


B  -{-  G  H-  ^.  _  ^  ^ 

7r+7,^"+  n  ~  tail >,' 


assuming  that  a  tangent  galvanometer  is  used. 

From  this  eijuation  calculate  the  resistance  li  -\-  ('. 

Afake  similar  observations  with  another  battery,  and  calcu- 
h.te  the  resistance  of  7j,  +  <r  from  equation 

B,+  a   f  li,  ^  tan  e, 
B\  +  V/  +  Pi,       tan  fv; 

B  l.'einf  a  second  battcrv.  (^   and  W.  the  mean  defiections. 

1  O  •■  « 


:sm;i.'"'  '»e-:«:"  '  '%-eK^asa'^r^  ■ 


3.'.  i«!i 


ELKCTllICriY. 


•231 


Tliese  observations  will  also  give  the  ratio  E/E,  by  taking 
one  observation  in  each  case,  e.g., 

E  _  {B  -\-  G  +  It)  tan^ 
E,~  {B,-\-  G  +70'tHn^.' 

Substitute  ior  B  +  G  and   B,  +  G  the  values  found,  a 
for  li  and  R^  the  resistances  unplugged  from  the  box. 

Assume  the  electromotive  force  of  the  Daniell  cell  to  be 
1.08,  and  calculate  that  of  the  other. 

Compare  with  the  Daniell  cell,  a  Leclanchu,  a  dry  bat- 
tery, a  storage  battery. 

Example. — Enter  results  thus : 


Battery. 


DHDiell. ..  .. 
Leclancbe . . . 
Dry  battery. 
Storage-cell 


R 

A'. 

» 

•i 

B  +  U 

K 

20 

40 

50.06 

33.56 

3.8 

1.08  ' 

30 

40 

60.20 

42.33 

i.y 

:.42 

20 

40 

42  45 

31.05 

20.3 

1.35 

30 

00 

63.00 

44.85 

.8 

2.25 

Blank  to  hejilled  in  hy  dndent. 


».         H+G 


ll 


m 


r. 


23: 


LAHOL'A  TORY  I'lIYSK'S. 


70.  COMPARISON   OF   THE    E.M.F.   OF   BATTERIES   BY 
POTENTIOMETER   METHOD. 

References. — As  in  last  experiment  and,  in  addition,  S. 
Thompson,  p.  -i-'l. 

Apparatus  Required. — A  sensitive  galvanometer;  a  po- 
tentiometer; a  tliree-way  plug-key;  a  storage  battery;  a 
batterv  <>f  constant  E.  M.K. ;   l»atteries  for  comparison. 

Theory  of  Experiment. — Sui)pose  7:'  a  battery  of  constant 

E.M.F. ,  the  poles  of  which  are 
Connected  to  a  wire  AB  of  re- 
Q   sistance  Ji,  A  being  tlie  negative 
pole. 

Let  the  resistance  of  the  bat- 
tery uTid  connection  be  denoted 
by  /■;   then 


('  = 


/.'  + 


/' 


If  the  negative  p<»le  of  any  other  battery  of  E.M.F.  /T, 
be  connected  to  A  and  tlirongli  a  galvanometer  to  a  point  F 
on  AB  snch  tliat  no  current  How  through  the  galvanometer, 
then  the  E.M.F.  of/.',  must  be  equal  to  the  difference  of 
|)otential  between  A  and  P  produced  by  the  battery  E. 


Hence 


C  = 


Ji, 


if  7i,  be  the  resistance  of  AP 
Hence 


Ii\ 


E 


(1) 


R-\-r 

li  r  be  negligible  as  compared  with   R^  or  of  known 
value,  the  ratio  /f  to  E,  onn  tlnis  be  determined. 


^[%!^^''sSxs^KS?^y^l^!^er^^saxm■ifi£^ptn^^s.w^..  • 


.'iVTj?','  ■.'  o*^   cai 


BLECTimiTY, 


M  anotlier  battery,  7^',,  be  similiirly  connected,  and  a  point 
/',  be  found  such  that  no  current  passes  tlirougli  the  galva- 
nometer, then 


Hence 


F 


K 


li^r 


-/?. 

/••; 


(2) 


a  comparison  of  E^  and  A,  independent  of  r. 

Practical  Directions. — Connect  to  the  ends  of  a  potenti- 
ometer-wire tlie  poles  of  a  storage  l)attery  E^  Fig.  49,  witli 
negative  pole  at  A. 

Connect  the  negative  pole  of  a  battery,  /.',,  M'ith  which  the 
others  are  to  be  compared,  to  yl,  and  through  a  three-way 
plug-key  to  a  galvanometer  which  is  co.inected  to  the  sliding- 
contact  on  the  potentiometer. 

Connect  to  A  and  the  galvanometer  another  battery,  E^ , 
through  the  third  connection  of  the  three-way  kev. 

Adjust  the  sliding-contact  so  that  when  E^^  is  connected 
throuirh  the  galvanometer  no  deflection  is  obtained. 

Read  the  distance  AP  on  the  scale  attached  to  the 
potentiometer. 

Connect  /;',  with  the  galvanometer,  and  adjust  again  for 
•  d:-tlection. 

Read  the  length  AP^  as  before. 

Denote  these  lengths  by  /,  and  /,. 

Now,  since  the  wire  of  the  potentiometer  is  uniform. 


Hence 


E  = 


fy.E. 


?rmLi^xiJ^s  i^'^fiets&'^'-^v^'f'naiS':. .  -: 


flT- 


t  i 


•234 


LABURATUllY  PllYSlCi^. 


Xow  replace  E^  by  another  battery  ii',,  aiul  compare  as 
before. 

K  =  ^  X  /;.. 

For  each  comparison  the  length  l^  should  be  verified. 

Compare  witli  a  Daniell  cell  {E,)  as  standard  the  cells 
given,  A  Clark  cell  is  preferable  to  a  Daniell  if  the  api)ara- 
tus  be  suitable.  In  this  case  care  must  be  taken  not  to 
short-circuit  the  Clark  cell. 

Example. — Enter  results  thus : 


Batttry 

Clark  cell... 

Daniell 

Leclancbe  . , 
Bunsen .... 
Bicliroinat<>. 

Grove 

Dry  battery. 


1 

//388.0 

E 

388.0 

1.434 

293.2 

.75a 

1.08 

878.8 

.976 

1.40 

513.5 

1.323 

1.90 

554.7 

1.430 

2.05 

514.1 

1.325 

1.90 

351.8 

.906 

1.30 

Blank  to  he  filletl  in  hy  student . 


Battery. 

I 

I'h                     E 

L«n  kftri'  ^A'^B^JTi'iaei  'AjAT-t-  - 


KLELiiucrrr. 


fio 


71.  TO  CALIBRATE  AN  AMMETER,  BY  MEANS  OF  A  GAS- 
VOLTAMETER. 

References. — S.  Thoin]>soTi,  p.  209;  Nichols  and  Franklin. 
vol.  II.  p.  89;  Ilastin-fs  and  IJeach,  p.  421. 

Apparatus  Required. — A  gas- voltameter;  a  couple  of 
storage-cells  or  other  isuitiil>le  source  of  E.M.F. ;  a  rheostat; 
a  reversing-key  ;  a  stop-watch;  the  galvanometer  or  aiiiuieter 
which  is  to  be  calibrated. 

Theory  of  Experiment. — If  the  ammeter  or  galvanometer 
to  be  calibrated  be  connected  in  series  with  any  standardizing 
instrument,  the  indications  of  the  latter  being  proportional  at 
any  instant  to  the  current  passing  through  it,  the  indications 
of  the  first  instrument  may  be  reduced  to  their  value  in  cur- 
rent, or,  in  other  words,  the  instrument  nuiy  be  calibrated. 

The  present  experiment  is  one  of  relati'  ■■  cnlibration  only. 
For  this  purpose  a  convenient  standardizing  instrument  is  a 
form  of  gas-voltameter  devised  by  Prof.  Ayrton.  In  this 
voltameter  the  electrolytic  chamber  is  sealed  up,  and  the  rate 
at  which  the  mixed  gases,  hydrogen  and  oxygen,  are  given 
off  is  observed  by  the  rate  of  rise  of  the  electrolyte  in  a  tube 
whose  lower  end  reaches  to  the  bottom  of  the  electrolytic 
chamber.  The  tube  is  graduated  above  the  voltameter,  and 
the  time  required  for  the  liquid  to  rise  through  a  given 
number  of  divisions  is  inversely  proportional  to  the  current 
passing  through  the  voltameter. 

Therefore,  h^^'  any  given  current  through  the  voltameter 
and  ammeter  in  series,  the  reciprocal  of  the  time  taken  to 
rise  througli  one  <livision  is  a  measure  of  the  current  producing 
the  corresponding  deflfction  of  the  animator. 

A  curve  can  therefore  be  plotted  co-ordinating  the  re- 


ii.'JO 


LABOBATOJtY  l'UYi<lC:i. 


cii)rocal8  of  these  times  and  their  correHixnuling  ftnmieter 
detlections.  This  curve  is  a  relative  calibration  curve  for  the 
auinieter. 

If  an  absolute  calibration  were  re<iuired,  it  would  be  neces- 
sary to  determine  the  quantity  of  gas  deposited  in  a  given 
"me  and  to  calculate  the  current  corresponding  to  each  detiec- 
lun. 

Practical  Inactions. — Connect  the  gas- voltameter,  the 
source  of  E.M.F.,  and  the  rheostat  or  other  adjustable  resist- 
ance in  series  through  a  reversing-key  to  the  ammeter,  so 
that  the  current  may  be  reversed  through  the  ammeter  with- 
out reversing  it  through  the  voltameter. 

Start  with  a  large  current  through  the  instrument  suffi- 
cient to  ^ve  60  or  70  deflections. 

If  possible,  read  both  ends  of  the  nuedle,  tf,  tf,. 

Observe  with  the  stop- Match  the  time  required  for  the 
electrolyte  to  rise  from  the  bottom  graduation  on  the  tube  to 
the  top  one.  If  the  instrument  be  one  in  which  deflections 
can  be  read  on  both  sides  of  the  zero,  reverse  the  current  and 
as  before  read  both  ends  of  tlie  needle,  tf,,  rf,,  and  the  time 
of  rise  of  the  electrolyte. 

Repeat  the  observation  for  a  number  of  different  deflec- 
tions. 

This  can  be  doi  e  by  varying  the  resistance  in  the  circuit. 

With  the  smaller  currents  it  will  not  be  necessary  to  wait 
until  the  liquid  has  risen  through  the  whole  length  of  the 
tul)e,  but  can  be  taken  through  a  few  of  the  graduations  and 
the  time  it  would  take  for  the  whole  calculated. 

Plot   a   curve   with    galvanometer    deflections    (^)     for 

abscissas,  and  reciprocals  of  times  ,.    for  ordinates. 

Precautions. — If  tlie  aiumeter  has  a  single  turn  or  only  a 
few  turns  in  its  coil,  it  will  be  necessary  to  connect  it  so  that 


ELECTRICITY, 


237 


tlic  rest  of  the  apparatus  is  at  least  a  meter  distant  from  it. 
Otherwise  tlie  current  in  that  part  of  tlie  circuit  will  afiect 
the  aniineter  readings. 

Do  nt»t  short-circuit  the  storage- battery. 

Example. — Knter  results  thus: 


i 

<, 

6.5 

7.5 

9 

10 

11 

12.5 

16 

17 

26 

25.5 

39 

39.5 

53 

54    ' 

62 

1 

61 

1 

«, 


7.5 
10 
10 

n 

24 
Al 

50.5 
64 


8. 
10. 
11 
18. 
24. 
42 
51 
«5 


7.5 
10  1 
11.1 
17.1 
25 

40.7 
52  3 
62  7 


<•' 


234 
155 
131 

84 

45 

25 

]5 
8.5 


.00431 

.0064 

.0076 

.0119 

.0232 

.04 

.066 

.116 


Blank  io  he  jiUcd  in  by  atudent. 


,_  . 

1 

t 

i 

<1 

». 

<> 

e 

t" 

t 

Sbow  cuiTC. 


l-§ 


288 


LABOtLA Ton Y  PU  YSICS. 


72.   TO  DETERMINE   THE    CONSTANT   OF    A    SIEMENS 
ELECTRO-DYNAMOMETER. 

References. — S.  ThoiniK-ion,  j).  ;5'.»2 ;  Hastings  and  Heacli, 
p.  4'j;{-,  Mit'liols  uiid  Franklin,  vol.  11.  p.  "ill  ;  Anthony  aiid 
l>ni('k»'tt,  |».  .■>.■|^;    Haikor,  y.  "*.♦.■». 

Apparatus  Required. — An  olectro-dynainonieter;  a  copper 
voltuim't«'r;  a  .stonige  Imttery  of  two  colls ;  a  reversing-switcli ; 
!i  >top  watch  :  a  rheostat. 

Theory  of  Experiment. — If  a  current  (1  is  sent  in  neries 
tliion<rh  tlic  tixcd  iuid  niovahle  coils  of  a  Siemens  electro- 
dynamometer,  we  have  the  relation 

V  =  h'e, 

where  W  is  the  angle  through  which  the  torsion  index,  to 
which  the  spiral  sjtring  is  attached,  must  he  turned  to  ])alance 
the  torque  due  to  the  current,  and  A'  the  constant  of  the 
instrument. '    E(puition  (1)  may  he  evidently  written 

If  r'he  measurecl  and  ^  o])8erved,  K  can  he  calculated 
from  formula  {'!). 

The  current  ('  may  he  measured  eitlicr  hy  a  voltameter, 
a  Kelvin  balance,  or  a  standard  Weston  instrument. 

We  shall  assume  that  a  copi)er  voltameter  is  used. 

In  this  case  the  value  of  /I'is  given  by  the  equation 


K^ 


7)1 


t  X  .0008280  X   V^ 


wliere  w  is  the  mass  of  copper  deposited,  and  t  the  duration 
of  thu  cuiTout  in  su<H)nds. 


WPWPl 


m 


wmm 


Ki.KcriiiriTY. 


-I'M) 


Practical  Directions — Set,  l.y  incuiis  i.f  a  coinpuHs,  the 
plane  of  tlio  tiiovahlo  coil  of  the  electro-dynainoineter  ap- 
proxiiiiatfly  at  rijrlit  angles  t<.  the  magnetic  meridian. 

Level  the  instrnment  so  tlmt  this  coil  swings  freely. 

Turn  the  torsion  index  up  against  the  stop,  a?id,  if  the  in- 
'runient  he  projKirly  adjusted,  the  needle  nirried  hy  the  coil 
ill  remain  at  zero. 

if  not,  loosen  the  collar  which  carries  the  pointer  and 
adjust  the  toi-sion-head  until  the  needle  is  at  zero  with  the 
pointer  against  the  stop. 

See  that  the  mercury  cups  at  the  terminals  of  the  uk.v- 
ahle  coil  are  full,  and  that  the  ends  of  the  coil  dipping  into 
them  are  well  amalgamated. 

To  set  the  plane  of  the  movaltle  coil  acniratt'lv  at  right 
angles  to  the  tiu-ridian,  connect  the  coils  in  serie>.  through 
the  reversing-switch  and  rheostat,  to  the  hattery.  and  I»alance 
the  current. 

On  reversing  the  current  the  needle  should  return  to  zero. 
If  not,  turn  the  wliole  instrument  until  it  tloes. 

Coimect  the  dynajuometer,  hattery,  rheostat,  ami  voltam- 
eter in  series,  and  adjust  the  current  to  200  degrees  a[»prox. 

Open  the  circuit. 

Clean,  wa^h,  and  weigli  the  copper  ])late  of  the  voltam- 
eter on  which  the  copper  deposit  is  to  be  made,  and  replace 
it  m  the  voltameter. 

Close  tlie  circuit,  taking  the  exact  time. 

Allow  the  current  to  run  for  at  least  20  minutes,  keeping 
the  dynamometer  continually  halanced  I>y  adjusting  the  con- 
tact piece  of  the  rheostat. 

Headings  should  he  taken  every  two  minutes  to  allow  for 
small  changes  of  the  current. 

vV  mean  of  the  readings  gives  the  true  value  of  0, 
Open  the  circuit,  taking  the  e.xaot  time. 


540 


LA liORA  Ton  Y  PHYSICS. 


Wftsli,  dry,  and  weijrli  tlio  ciitli<H;o  to  i'„  of  n  prniii. 

Two  such  dt'tertniriutioiia  slionlU  bo  made  with  dilTerent 
deflections. 

A  mean  of  the  coiiiitant!*  should  he  tiikeii  for  IC. 

Precautions. — The  eoniiet'tioiis  to  the  dynainoiiieter  hliould 
hi'  made  with  tliiii  wire,  utid  the  switch  and  rheoftut  kept 
at  hoiiie  distaiu'o  fnuii  it,  otherwibo  the  instrument  will  lie 
alfected  hy  the  I'lineiits  in  *he  c.xteriuil  circuit. 

The  dynamometer  fihould  al.-io  ho  kept  away  from  strong 
niiignets. 

Keep  the  dynamometer  always  in  an  upright  position. 

Example. — Enter  results  thus: 


HIEMENS  DYNAMOMETEU  No. 


H' 

M-. 

m 

1.844 
.751 

t 
MiniiieH, 

T'Tsion 
I.iilrx. 

K 

51.4f<9 
53  3:52 

53.8:12 
54  083 

r.o 

80 

Mean  of  15  rHaii'gs 

216.47 

33.00 

,213 
.221 

Ml'iid 

value 

.217 

Blank  to  he  filled  in  hy  student. 


w 

111 

1 

t 
Minutes. 

Torsion 
Index. 

K 

Mcfin 

value 

f7^'^v 


ELECIRICITY. 


241 


73.    TO    CM.IBRATE    AN    AMMETER    BY    A    SIEMENS 

DYNAMOMETER. 

References,— As  in  Experiineiit  72,  aiid,  in  ui!  'itioii,  S. 
TliuiHp.-oii,  i>.  L'o'.t;  Hiistiiijrs  and  Ik-acli,  j).  i!41  ;  McIdIs 
aiKJ  FraulJiii,  \(>I.  11.  j).  ,si>. 

Apparatus  Required. — A  Siemt'n,s  (Iviumionu'tc  r;  uii  iim- 
iiictir  ul'  u|>|>r().\iiiiiiteiy  tlio  Biiiiie  rim  ire :  a  rliioatut  of  suitable 
ri'sistiiiiee;   a  storage  battery  of  several  eells. 

Theory  of  Experiment — Knowing  the  eonstant  of  tiie 
(lynanu)nieter  it  ean  be  used  very  conveniently  as  a  standard- 
izing instrument.  If  the  instrument  to  be  calilirated  is  of 
approximately  the  baine  range  as  the  dynamometer,  it  mav 
simply  l»e  conneeted  in  series  with  it,  and  the  two  in^t^ument8 
read  simultaneously  at  suitable  intervals  throughout  the  raiK'c 
The  sijuaro  root  of  the  reading  of  the  dynamometer,  multi- 
]»lied  by  its  constant,  give  the  correct  value  of  the  current 
for  the  corresponding  indication  of  the  ammeter,  which  may 
be  either  a  direct-current  or  alternating-current  instrument. 

Practical  Directions Vdjust  the  dynamometer  as  in  the 

last  experiment. 

Set  up  the  ammeter  and  level  it  until  the  needle  swini's 
freely  ami  comes  to  rest  at  zei'o. 

Connect  the  coils  of  the  dynamometer  in  series  with  the 
anuneter  through  the  rheostat  an<l  battery. 

Adjust  the  current  to  the  initial  readuig  of  the  ammeter, 
sually  in  the  5-amp. -range  instruments  this  readln"  is  O.;") 
amp. 

Malance  tiie  dynamometer  and  read  both  insiruments. 
Continue  to  take  readings  at  intervals  of  O..")*)  amp.,  as 
indicated  bv  the  ammeter. 


^^fcETTol 


S  *' 


3, 


242 


LAHOKATOBT  PHYSIC8. 


Calculate  the  currents  corresponding  to  the  indications 
of  the  ammeter. 

Plot  a  curve  with  ammeter  readings  for  abscissas,  and  the 
differences  between  the  ammeter  reading  and  the  correspond- 
ing currents  as  deduced  from  the  dynamometer  readings  for 
ordinates. 

Example. — Enter  results  thus : 

Ammeter,  Soames  &  Nalder,  range  5  amps. 

Siemens  Dynamometer,  range  4  amps. 

Dynamometer  constant  as  previously  determined  0.217. 


Dyn.  BeadiDK. 

Am.  Reading. 

Calculated 
Cun-eat. 

Dlfferr 

7.7 

.4 

.62 

+  .18 

18.0 

1.00 

0.92 

-.08 

42.0 

1.50 

1.40 

.10 

78.0 

2.00 

1.89 

.11 

115.6 

250 

2.88 

.17 

147.0 

2.90 

2.64 

.26 

228.6 

8.56 

8.28 

.27 

368.0 

8.95 

8.58 

.27 

825.0 

4.85 

8.91 

.44 

Blank  to  he  jtlled  in  hy  stxtdent. 


Dyn.  Reading. 

Am.  Reading. 

Calculated 
Curreut. 

Difference. 

Show  curve  as  indicated  ahove. 


ELECliaClTY. 


243 


74.  THE  D'ARSONVAL  GALVANOMETER TO  DETER- 
MINE ITS  RESISTANCE  BY  SHUNTING  IT  WITH 
KNOWN  RESISTANCES. 

References.  —  As  in  ExiHjriment  75  and,  in  addition, 
Jiarker,  p.  7<>4:  Carhart,  pt.  ii.  p.  270;  Knott,  j)t.  n. 
p.  l!»0;  Nieliolsand  Franklin,  vol.  ii.  p,  5(i;  Watson,  p.  6!»4; 
S.  Thompson,  j>.  401);  Hastings  and  Beach,  j).  420;  An- 
thony and  Braekett,  p.  301. 

Apparatus  Required — A  D'Arsonval  galvanometer,  with 
lamp  and  scale;  a  resistance- box  of  100,000  ohms;  a  resist- 
ance-box of  2000  ohms ;  a  storage  battery  or  other  suitable 
source  of  current  ;  a  thermometer;  a  reversing-switch. 

Theory  of  Experiment — In  the  D'Arsonval  galvanometer 
the  detlection  of  the  galvanometer  depends  on  the  strength  of 
the  magnetic  field  in  which  the  coil  hangs,  the  number  of 
windings  in  the  coil,  and  the  current. 

Since,  for  small  deflections,  the  njagnetic  field  in  which 
the  coil  swings  may  be  considered  uniform,  the  current  may 
be  taken  as  proportional  to  the  deflection,  or 


6'=A'rf., 


where  C  is  the  current  in  the  coil,  and  '?,  the  scale  <h'fle('ti<>n. 

Suppose  a  galvanometer  (i,  a  laryc  lesisiiuice  /.', ,  a  iiat- 

tery  of  E.]\I.F.  A'  to  be  connected  in 

series,  and  tlie  galvanometer  shunted 

by    a    resistance  .V  :    then     the    total  -^B  { — -JG  IS, 

current  in  the  circuit  is  given  by  the 
e<iuatiou  Fia.  50. 


4' 

■    I. 


»      { 


244 


LAliUliA  TOR  Y  PU  Y81CS. 
E 


6'  = 


as,  ' 


aud  the  current  liowiiig  through  the  galvanometer  is  given 
by  the  eciuatioii 


E 


(1) 


If  now  ^S',  and  A',  \ye  changed  to  >S',  and  ^,,  and  the  de- 
flection to  <y„  we  have  again  tlie  current  in  the  galvanometer 
given  by  tlie  e«|uation 


v.-     '' 


E 


o^  +  .v. 


s, 


In  practice  it  is  convenie.it  to  make  5,  =  -^,  and  to 
adjust  S,  until  the  deflection  *,  is  nearly  equal  to  tf,,  so  that 

9  1        I  ' 

where  a  is  a  small  difference. 

If  the  current  be  not  proportional  to  the  deflection,  the 
last  adjustment  eliminates  any  error  on  that  account. 

Dividing  (1)  by  (2)  and  substituthig  6,  +  «  for  <J, ,  and 
2.B,  for  ^, ,  we  have 


mMi^8iap^«- 


BLECTHtCITT. 


245 


S. 


Solving  for  G,  and  neglecting  —  .  ~,  since  a  is  small 
as  compared  with  rf, ,  and  S^  as  compared  with  E^ ,  we  obtain 


(4) 


a  form  convenient  for  calculation. 

Practical  Directions. — Set  the  galvanometer  on  a  bracket 
or  pier  free,  if  possible,  from  the  vibrations  of  the  floors  of 
the  room. 

Carefully  level  the  instrument  until  the  coil  swings  freely. 
The  coil  of  the  galvanometer  should  hang  with  its  plane  ap- 
proximately parallel  to  the  plane  of  the  magnet.  Any  adjust- 
ment for  this  purpose  may  be  made  by  means  of  the  torsion 
head  to  which  the  suspension  is  attached. 

Set  the  lamp  and  scale  fibont  a  meter  from  the  galva- 
nometer and  obtain  an  image  of  tho  cross-M-ire  on  the  scale. 

If  the  image  be  not  sufficiently  clear,  a  suitable  spectacle- 
lens  should  be  selected  and  placed  in  front  of  the  cross-wire 
so  as  to  bring  it  into  focus  on  the  scale. 

Set  the  scale  at  right  angles  to  the  line  joining  its  middle 
point  to  the  mirror,  the  planes  of  the  mirror  and  scale  being 
l)arallel.  This  can  be  done  by  adjusting  the  position  of  the 
scale  until  its  ends  are  equidistant  from  the  sasponsion,  the 
image  of  the  cross-wire  being  at  the  middle  of  the  scale. 

If  there  is  not  a  thermometer-hole  through  the  case  of  the 
instrument,  the  thermometer  should  bo  placed  as  near  the  coil 
as  possible. 

Connect  a  two-volt  storage  battery  or  a  couph?  of  dry 
cells  through  a  reversinir-swifcli,  in  scries  with  the  L'alva- 
nomcter  and  a  risistaiuc  /.*  nf  fmiii  iir»,O0(>  to  .mIjOoo  uhuis. 


■* 


I 

«■    I 


246  LAUOIiATOIiY  PHTSICS. 


Shunt  the  galvanometer  w  itli  a  shunt  S^. 
The  uouuectiuus  are  shown  in  Fiiriire  51. 


Adjust  the  shunt  so  as  to 
obtain  a  detlection  of  about  300 


Fig.  51. 
readings  gives  rf,. 


X     -=:  scale  divisions. 


Reverse    the    current    and 
read  again.    The  mean  of  the 

Now,  change  the  resistance  in  the  box  /?,  to  --'  and  adjust 

the  shunt  S,  until   a   deflection  as   nearly   eijual  to   d,  as 
possible  is  obtained. 

Reverse  the  current  and  read  again. 
The  mean  reading  gives  rf,. 

a  =  tf.  -  <y. 

Repeat  the  first  set  of  readings  again  to  determine  whether 
changes  in  the  temperature  of  the  resistances  used  or  in  the 
coil  or  in  the  E.  M.  F.  of  the  battery  have  occurred,  and,  if 
a  small  change  has  occurred,  take  the  mean  of  the  first  and 
third  set  of  readings  for  rf,,  keeping  li  and  N' unchanged. 

Take  the  temperature  of  the  galvanonicter. 

The  teinix?rature  of  the  shunt  should  in  eaeli  cjise  be  taken, 
and  corrections  made  in  its  resistance. 

Example.— Enter  results  thus: 

Nalder  galvanoiiifter  88"28.  Scale  distancp  103  5  cm. 
Sl-nnt-lxix  platinum  silvpr.  No.  3750.  Correct  at  17°. 
Temp,  coefficient  of  sLunt,  0.00027. 


ELECTRICITY 


247 


Ri 

S.               «i 

Rt 

St 

«. 

■^T 

Temp. 
Shunt. 

Q 

50.000 

500 

801. 8R 
801.0  L 
802.0  R 
801.6  K 
801.4  L 
808.0  K 

25.000 

127 

302.7 
801.6 
303.5 

19.0 

19.3 

256.1 
at 
19- 

Mean 

301.8 

808.6                   a=0.8 

1 

Blank  to  he  filled  in  by  sitidetit. 


K, 

s. 

*. 

Ht 

St 

t. 

Temp. 

ami. 

Temp. 
ShiiDt. 

a 

Msaii. 

ar  = 

1 

75.  TO  FIND  THE  CONSTANT,   K,  OP  A  D'ARSONVAL 

GALVANOMETER. 

References.— S.  Tliompson,  p.  205 ;  Barker,  p.  779 ;  Hast- 
ings and  Beach,  p.  419;  Carhart,  pt.  ii.  p.  338;  Nichols 
and  Franklin,  vol.  n.  p.  46. 

Apparatus  Required. — A  D'  Arson val  galvanometer ;  a  tan- 
gent galvanometer  or  copper  voltameter :  a  standard  l-oliiu 


I 


m 


n 


248 


LAB0HAT0R7  PHYSICS. 


resistance- coil ;  a  20,000-olim  box  of  resistiiiice-coils ;  a  storage- 
battery;  a  reversing-switch ;  tliree  tlierinoiiieters. 

Theory  of  Experiment — If  a  standard  cell  of  constant 
E.M.F.  ^  be  connected  in  series  through  a  large  resistance 
R,  and  the  galvanometer  Gy  giving  a  dellection  6,  then 


or 


£:= 


E 


(A*^G-\-  B)d 


•  • 


(1) 


If  E,  Ji,  O,  B  be  known,  A' can  be  calculated. 
K  can  be  determined  in  this  way  by  using  a  standard 
Daniell  cell  and  about  25,000-ohin  resistance. 

For  purposes  of  accuracy,  however,  the  Daniell  cell  is  not 
sufficiently  steady,  and  the  following 
method  is  preferable. 

If  a   known    current   C  be  passed 
through  a  standard  resistance  r,  the  ter- 
minals of  which  are  connected  through 
Xi    a  high  resistance  li  to  a  galvanometer 
(see  Fig.  52),  the  current  c  through  the 
galvanometer  will  be  given  by  the  equation 

Cr  ^,.  „  Cd 


/h 


c  = 


n  +  g 


^KS, 


or 


K  = 


{It  +  j/)rf' 


(2) 


where  g  is  the  resistance,  A'  the  constant,  and  S  the  deflection 
of  the  galvanometer. 

Ji  -{-  g  must  be  lari^e  compared  witli  >',  and  g  must  be 
determined  beforehand,  if  not  ulreadv  kiiuwii. 


'%-  .xiif -i^.^E^^'^^ssf^;^ 


•<*ity»  -jMTHeC'if^ 


=i-JIW5i'^r^*^MS3HM 


BLBCTRWITT. 


249 


Practical  Directions.— Set  up  the  galvanometer  as  de- 
scribed in  last  experiment,  and  make  connec- 
tions as  shown  in  J'ig.  53,  r  being  the  standard        •" Y/) 

one-ohm  coil,  and  B  a  storage- battery.     O  is   ^  \ 

the  instrument  used  for  measuring  the  main    ^ 
current.  y\/\/\/\/\A/v 

If  a  tangent  galvanometer  be  employed  for 
this  purpose,  instructions  for  its  use  will  be 
found  in  the  experiment  on  "Absolute  Meaa-  ^ 
urement   of  a   Current  by  Tangent   Galvan- 
ometer."     If  a  copper   voltameter  be  used, 
proceed  as  in  previous  exi>eriment  with  copper 
voltameter.    A  deflecting  instrument  for  meas- 
uring the  current  is,  however,  more  convenient 
for  this  experiment.    In  either  case  the  method  of  procedure 
is  as  follows : 

Adjust  the  galvanometer  current  by  the  resistance-box  H 
till  a  conveniently  large  deflection,  of  about  300  scale-divisions, 
is  obtained. 

Three  galvanometer  readings  should  be  taken,  the  current 
being  reversed  each  time. 

Should  a  deflecting  instrument  be  used  in  measuring  C,  it 
must  be  read  simultaneously  with  the  D' Arson val  galvan- 
ometer. 

The  whole  set  of  readings  should  be  taken  twice. 

If  a  copper  voltameter  is  being  used,  the  current  should 
be  left  running  for  twenty  minutes,  and  readings  of  the 
galvanometer  on  reversal  taken  every  two  minutes,  to  allow 
for  continual  small  changes  in  the  current. 

Also  the  reversing-switch  must  be  placed  in  the  galvan- 
ometer circuit,  and,  unless  an  instantaneous  reversing-switch 
be  used,  time  must  be  allowed  in  the  calculation  of  C  for  the 
reversals. 


^KT..  \^'3v  ;- w^' 2g»H«rx5aaEiSKB?'iJi»«aHWE®?; 


..ii'= 


.;ti':».--*-^GS*.Vif 


f 


1^ 


250 


LABORATORT  PHYSICS. 


In  either  case,  a  mean  of  all  the  galvanometer  readings 
should  be  taken  for  rf,  and  a  mean  of  the  main  current  read- 
ings for  C. 

The  temperature  of  the  shunt  r,  galvanometer  g,  and 
resistance  li  should  be  noted  at  the  time  of  observation,  and 
corrections  made  for  them  in  the  calculations  if  necessary. 

The  scale  distance  should  be  carefully  measured  and  ru 
corded. 

Example — Enter  results  thus : 


DAR80NVAL  GALVANOMETER,  NALDER  No.  8688. 
Data  given  by  w*aA«r*.— Resistauce  of  galvanometer  is  261.95  ohms  at 
24°.7  C.     Reslstuuce  r,  one  ohm  box  No.  »««0,  platinum-silver,  correct  at 
18.    Reslstuuce  R,  platinum-silver  box  No.  8750,  correct  at  17'.0  C. 


R 

(of 
R 

(of 

r 

t 

tot 
D'Arg.  0. 

Tangent  OalTanoinet«r. 
n=  10. 

t 

Radius. 

11,000 
11,000 

19.00 
19.» 

18.4 
18.4 

340.6  L 
333.0  R 
338.6  L 

837  5  L 
328.0  R 
383.8  L 

17- 

47.8 
47.4 
47.8 

46.7 
46.8 
46.7 

18.2 

Mean  results,  Ist  set 

836.3 

47.88 

Mean  results.  2d  set 

881.8 

48  73     1 

1 

„      10^ (Radius)  X  tan  0 


Ist  set, 
2d  set. 


=  .466, 

^^ ^71    _  _£ 

(11,000  +  •>6.')  336.3  ~  8041000 "^"P" 

=  1  volt  through  8.041/2,  Ist  Mt. 
466^ 1 

(11,000  +  86-.i)  bSlTS     msium  """p* 

=  1  volt  through  8.028A. 


/^-.y-s'i!  'ly  =    .•■s»\^'wyt' 


cen£*<ttj%.    "ivvvi'? 


BLECrRJCITT. 


251 


Blank  to  he  filled  in  by  student. 


C  = 


jsr  = 


R 

<of 

R 

(of 
»1 

i 

(of 
D'Am.  G. 

Tangent  Onlvanuiiicter. 
It  = 

* 

1 
Radiiig.     1 

1 

Meau  results,  Ist  set 

Mean  results,  2d  set 

76.    TO  CALIBRATE  THE  SCALE  OF  A   D»ARSONVAL 

GALVANOMETER. 

References — As  in  previous  experiments. 

Apparatus  Required — A  D'Arsonval  galvanometer;  two 
small  resistancc-lioxos;  a  10,000-ohm  coil;  a  reversing, 
switch ;  a  storage  battery  or  Daniell  cell ;  a  rheostat ;  a  tan- 
gent galvanometer,  or  a  sensitive  galvanometer  with  a  poten- 
tiometer and  Clark  cell. 


r 


ill 


252 


LA  BOH  A  TOH  r  PHY8ICa. 


Pro.  54. 
is  constant 


Theory  of  Experiment. — The  deflections  of  a  D'Arsonval 

galvanometer  are  not  accurately  projwrtional  to  the  current. 
It    ia   necessary,   thei-efore,   to   calihi-ate  tli 
scale  that  is  to  determine  the  corrections  to  he 
ajtplied  for  each  scale  reading. 

Supjxkse  a  constant  current  to  be  passed 
through  two  resistances,  It  and  »y.  as  in 
Fig.  .'>4,  S  beujg  connected  in  series  with  a 
galvanometer  and  a  large  re^igtance  R^. 

Sup])06e  S  so  small  as  compared  with 
/?,  that  any  small  variation  of  S  will  not 
materially  alter  the  current,  so  long  aa  7?+  *5 
Then  the  difference  of  potential  on  the  gal- 
vanometer terminals  will  be  proportional  to  the  resistance  8. 
The  deflections  of  the  galvanometer  will  therefore  also  be 
proportional  to  S,  jwsuming  that  the  deflection  is  proportional 
to  the  current. 

If  the  deflections  for  ditTereiit  values  of  S  be  observed, 
their  ditferences  from  propctrtionality  can  be  calculated  and  a 
correction  curve  plottetl. 

Practical  Directions. — C'onnect  the  galvanometer,  battery, 
and  resistances  as  in  Fig.  .5.'),  putting  the  reversing-switch  in 
the  galviin(»meter  circuit  only. 

If  the  source  of  current  used  be  not  as  constant  as  re- 
(juired,  it  can  be  kept  con.xtant  by  i)laciiig  in  the  battery 
circuit  a  rheostat  and  tangent  galvanometer,  and  adjusting 
continuously  the  rheostat  so  as  to  keep  the  deflection  of  the 
tangent  galvanometer  constant.  A  better  method  still  would 
be  to  connect  the  terminals  of  the  battery  to  a  high-resistance 
potentiometer  and  balance  it  continuously  against  a  Clark  cell. 
This  can  be  done  by  having  the  resistance  in  the  Clark-cell 
circuit  constant  and  adjusting  the  rheostat. 

The  connections  in  this  case  would  be  as  in  Fig.  55, 


BLKCTHICITY. 


253 


If  7?,  1)0  10,000  fdiiiiH  and  the  rehihtuiicu  *S'  varies  from  1 
to  10  oliiiiH,  Ji  -{■  .V  Ijeing  kept  coustiiiit,  the  iimiri  eircuit  re- 
Hwtiinco  will  vary  loss  than  .01  ohm  <hie  to  tho  chuiige  iti  -V 
and  tho  diilereuco  of  potential  on  tlie  gulvanoraoter  turminulh 


WWM lljh 

"     B 
Fi...  55. 

will  vary  less  than  j^'^^  from  proportionality  as  a  result  of 
this  change. 

The  work  of  tlie  rheostat  will  therefore  l)e  largely  to  com- 
jH'nsjite  fur  changes  in  the  K.M.K.  of  the  battery. 

Unplug  10,000  ohms  from  bux  /*',  in  galvanometer  cir- 
cuit, and  10  from  box  >'. 

Unplug  from  the  btjx  /.'  a  resistance  until  a  suitable  de- 
flection of  say  3.'»o  scale  divisions  is  obtained. 

If  the  constant   A'  luis  already  been  found,  as  in  previous 
experiment,    then   the   resistance    I!  may  be    adjusted    until 
the  same  d<'f'"ction   i>  obtained  as  that  for  which    A'  was  ca' 
culated.  and    tin-  dilb-rences  from  proj>ortionality  ciilenl.itfl 
with  rej'ai  d  to  it. 

Having  iibtaiiuMi  ,i  suitable  dcHirtion,  reverse  the  current 
and  mean  the  ii  idings,  to  elinnnate  errors  due  t<>  torsiiru. 
Xow  pliii;-  in  one  ohm  in  >' and  tinplug  one  in  I',  and  a<liii>t 
the  rheostat  mn  Utv  a  balance  against  the  (lark  cell, 

Kead  again  and  reverse. 

Contimie  the  process  right  down  the  seale. 

Calculate  what  the  detiection  should  i»e  in  each  case,  and 


^1 


ri 


:i;.4 


LA hoiu  rony  riirnirs. 


|»K»t  a  curve  with  »cale-rt'iulin;;«  a^  ahHciHriOii  atwi  dilTei-cnccH 
iiri  untinuteo. 

Tliu  caKMilatotl  (letlectioiis  will  l>o  ol»tuiiie<|  in  iwli  oawi  hv 
taking  iiiii,..tt'iitli«,  iMght-teritliH,  Hjveii-teiiths,  etc.,  of  the 
H"»*t  ili'tii'ctidii. 

Example. — Knter  rebult«  thim: 

D'Arnoiival  (ialvaiioiiiHcr,  No.  ;{<]'>8. 


I 

'i 
4 


Mraii 

10 

DfHrctiori. 

848.25 

«... 

818.2 

8 

278.8 

7 

848.0 

6 

808.2 

5 

178.3 

4 

188.6 

a 

104.1 

2 

1. 

0 

1. 

2. 

8. 

4. 

T) 

6. 


8. 

9. 

10. 


69.5 
84.9 

85 

69.5 
104.1 
188.5 
173.7 
206.8 
240.8 
275.1 
808.5 
343.7 


I'ali-iilattMt 
UrfltHJtion. 


845.5 
811.0 
276.4 
241.9 
•.'06.8 
17l.\8 
138. •■ 
108.6 
69.1 
34.5 

84.5 
69.1 
108.6 
188.2 
172.8 
207.8 
241.9 
276.4 
811 
845.5 


DiffcriMic*^ 


1  8 
1.4 
.9 
A 
.3 
.5 
.4 
4 

.5 
.4 
.5 
.3 

-  .1 

-  .5 
1.1 
1.3 
2.5 
2.8 


Ki.Kt'Tiw  irr. 


blank  fo  be  tilled  in  hy  student. 


25.'> 


I  'ot  curve  RH  directed. 


77.  TO  MEASURE  POTENTIAL  DIFFERENCES  BY  A  D»AR 
SONVAL  GALVANOMETER. 

References.     As  in  P^x|M'riiiii'iirs  74  ami  T.";. 

Apparatus  Required. —  A  iiMlvaiiDmctrr:  a  KMt.OiiO-olmi 
resi...tHiice-'K>\;  two  lo.OU(t-Mliiii  Im.v..s;  a  revorsiii«r,kev  •  a 
iimnlRT  of  Itatt'i-ies. 

Theory  of  Experiment.  -T^e  scale  of  a  D"  Arsutival  ^mha- 
noiretor  havi?\g  been  oalibrited,  the  values  AG  a:ul  K  detei- 
iniiied,  it  may  be  used  for  the  measurement  of  potentii<!  dif- 
ferences.    Witu  little   variation  <.f  method,  potential  differ- 


1, 

■a 


iiil 


yi  ■  C' 


250 


LABORATORY  POTSICS. 


ences  varying  from  a  few  micro-volts  to  the  volts  or  the  light- 
ing circuit  may  l>e  determined. 

I.  The  measurements  may  be  made  hy  connecting  a  large 
resistance  in  series  with  the  galvanon)eter  and  the  source  of 
current,  in  which  case 

1:=  K6{P-\-  G), (1) 


I  -^ 


i-^ 


the  terms  having  tlie  same  meaning  as  previous  experi- 
ments, where  A*,  /i*,  G  are  all  known  quantities  and  6  is 
observed. 

If  the  volts  on  the  lighting  circuit  be  determined  by  this 
method,  li  would  reiiuir-^  to  be  a  resistance  of  several  megohms. 
In  the  case  of  batteries  Ji  will  be  so  large  that  the  battery 
resistance  can  be  neglected. 

II.  Let  the  source  of  current,  B,  be  connected  to  a  large 
resistance,  Ji,  and  the  galvanometer  terminal  to  two  potential 
jx)ints,  A,  C,  of  tliis  resistance,  with  a  resistance  r  between 
them  (Fig.  56). 


Fui.  50. 


Then  the  current  through  the  galvamuneter  is  given  by  the 
e(|uatio'i 

A' 


C   :^ 


/?-/•  + 


r  ^f 


or 


ELJUvnuciTr. 


257 


(ii) 


.  t   Ii{r-\-0) 
In  practice  r  is  very  small  in  cumparigon  with  — — ^ — 


and  may  therefore  be  neglected. 


(3) 


III,  A  variation  of  this  metliod  would  be  to  put  a  resist- 
ance a,  in  series  witb  tlie  galvanometer.  This  would  neces- 
sitate making  A*  smaller  and  r  larger.  In  this  case  we  would 
liave  the  equation 

E  ..  r 


C  = 


7?  -  /•  + 


KA'.+  G)    ^  li,^  U-^rr 


=  Kii 


for  the  cun-ent  through  the  galvanometer. 
Solving  for  E,  we  obtain 

or,  neglecting  r  as  compared  with , 

,i-=«_«^±''il'->A-d..     . 


(4) 


(5) 


Equation  (5)  may  be  used  in  calculating  the  volts  on  the 
lighting  circuit,  equation  (4)  in  the  case  oi  bfittcrics. 

Practical  Directions.— 1 .  If  surticicutiy  lar^'o  resistances 
are  available  to  make  it  possiltje  t<>  olitain  readings  directly, 
connect  in  series  the  source  of  E.M.F.,  the  galvanometer,  and 
the  rcsiBtances. 


'J.>^ 


LABOBATORT  PHTStCP. 


If: 


Ii.  case  of  batteries  40,000  to  50,000  ohm«  will  l)e  neces- 
sary; in  case  of  the  lighting  circuit  a  resistance  from  2  to  8 
megohms  will  be  required. 

The  reversing-key  should  be  in  the  galvanometer  circuit. 
Do  not  close  the  key  until  you  are  absolutely  certain  that  the 
connections  are  correct  and  tlie  resistances  are  all  unplugged, 
otherwise  damage  may  be  done  the  resistance- boxes  or  the 
galvanometer. 

Read  the  deflection.  Reverse  the  current  and  read  again. 
Correct  the  readings  from  the  calibration  curve  in  each  case, 
and  take  the  mean  for  6. 

Measure  the  E.M.F.  of  each  of  the  batteries  given. 

If  the  lighting  circuit  l)e  direct-current,  measure  its  voltage. 

If.  Connect  the  source  of  E.M.F.  to  100,000  ohms  resist- 
ance, through  a  key,  which  must  be  left  open. 

Unplug  the  100,000  ohms  from  the  box  if  the  lighting 
circuit  is  to  be  determined. 

Coimect  the  galvanometer  terminals  to  the  potential-points 
hy  means  of  a  travelling  plug  on  the  box. 

If  the  box  does  not  contain  a  travelling  plug,  it  will  be 
neces.siiry  to  i)ut  in  a  small  resistance- box  in  series  with  the 
K  (0,000  ohms  and  use  it  for  adjusting  r.  In  this  case  Ii  will 
l.t  cjual  to  100,000  4  ;•. 

Adjust  /•  until  a  suitable  deflection  is  obtained. 

For  a  storage-battery  Ii  will  be  about  5000  ohms  and  r 
iiiM»ut  *J0  olinis. 

Repeat  the  observations  as  in  I. 

in.  Xow  put  10,000  ohms.  7?,, in  series  with  (?,  and  reduce 
/*'  to  10,000  and  adjust  as  l)cfnre. 

Make  a  diagrani  of  the  connections,  and  be  sure  you  under- 
stan<l  the  ooniu'ctions  before  proceeding. 

The  valu«?  of  /■  in  this  case  will  be  about  50  ohms  for  the 
lighting  circuit  and  about  'JaOO  for  a  storage-battery. 


ELECrmCITT. 


259 


Repeat  the  observations  aw  in  I  and  II. 

In  the  vahjes  sngjrested  for  /■,  R,  and  li,  above  the  galvan- 

ometer,  of  ^vhich  A' =  ^-|yr/2  and  ir  =  201.95  ohms  at 
24.7°  C,  is  referred  to.  The  stndint  can  easily  determine 
beforehand  approximately  the  corresponding  values  for  any 
other  instrument  once  its  constants  are  known. 

Precautions.— The  lighting  voltage  nmst  not  be  applied  to 
an  accurately  adjusted  and  valuable  resistance-box  without  at 
least  10,<M»()'ohms  being  unplugge<l.  IV  sure  that  the  connec- 
tions are  correct  Irt^fore  closing  the  circuit. 

Example.— Enter  results  thus: 

j^  -    _._  J_  __^.    a  (corrccieil  for  ifiupcratiire)  =  256. 


8  ()30,0<tO' 


M<-ili(><l 


Simrcf  of  K.M.F. 


'Ci.iTected  «     E.M  K. 

I 


1. 

11. 

III. 

1. 

11. 

111. 

1. 

11. 

Ill 


l.iirlitini:  circuit..   !2r.(KMt(i()i 
UMKMMl 
!      KHMIO     KXMMI 
Storn'M'-liuttcrv....'     r>0()U(> 

j  ..  I      KMKMi;    iniMlO 

l-eclanclu'    buttery  \      40«MM» 


lOOUU 


liHK)0 


;uo.5 

98.5 

10 

295.5 

97.9 

no 

365.4 

98.2 

354  7 

2.22 

20 

262.0 

2.25 

2500 

369 

2.23 

25».4 

1.30 

30 

21«0 

1.29 

2500 

215.2 

130 

Jiliiiik  to  hi   vUnJ  in  h>j  fitudcnt. 


Met  ho.  I 


1. 

11. 

III. 

I. 

H. 

111. 

I. 

11. 

111. 


Siiiiii'f  of  K.M  I". 


li 

^^ 

r 

Corm-tcl  .V    K.M.K. 


fl1 


m 


260  LABORATORT  PUYSICS. 

78.  TO  CALIBRATE  A  MILLI-VOLT  METER. 

References. — S.  Tliompson-,  p.  208;  Barker,  p.  720; 
Hastings  and  Beach,  p.  423. 

Apparatus  Required. — A  inilli-volt  meter,  two  single-cell 
storage- batteries;  two  resistance- boxes,  one  M'ith  an  olini 
divided  to  tenths;  a  potentiometer;  a  sensitive  galvanometer. 

Theory  of  Experiment. — The  calibration  of  instnnnents 
for  measuring  currents  or  potential  dilTerences  can  be  etTected 
by  means  of  tlie  calibrated  D'Arsonval  galvanometer  used  in 
the  previous  experunents  by  shunting  the  galvanometer.  The 
following  method,  however,  is  simpler  and  the  results  are 
more  easily  calculated. 


r 


H 


•  a. 


Z:> 


Bv 
Fig.  57. 

Suppose  P  and  P,  the  terminals  of  milli-volt  meter,  acro.'^s 
which  a  current  is  flowing  from  the  battery  /?,,  to  be  con- 
nected through  a  galvanometer  to  a  ])Otentiometer  (Fig.  .57), 
upon  the  terminals  of  which  is  »  constant  E.M.F.  A' ;  then  if 
the  sliding  contact  Q  be  adjusted  until  no  detiection  of  the 
galvanometer  is  obtained,  we  have  the  relation 


or 


r 

V 


Resistance  AQ 
Ilesistance  ^1  />' 

Resistance  .1  Q 
Resistauce  AD 


(1) 


BtECTRlClTY. 


261 


where  F  is  the  potential  difference  between  /*  and  P,,  and  E 
that  of  the  constant  hatteiy. 

If,  therefore,  the  indications  of  the  instrument  correspond- 
ini'  to  different  \iiUm»  of  I'  \>e  observed,  and  tiiese  indica- 
tions  be  compared  with  »#►  tjitW'ulatetl  vahies,  an  absohite 
calil)ration  cnrve  for  tht*  ItmKvnuttfttt  can  be  drawn. 

The  object  of  tlie  present  *-x{.*erinient  is  to  find  a  correc- 
tion curve  for  an  instnnuent  wliieii  has  already  been  cali- 
brated. 

Practical  Directions.— In  practice  it  is  necessary  to  have 
a  standard  Clark  or  We-xton  cfll  m  the  .system  us  well  us  tlie 
constant  battery  through  the  [>uientioineter.  For  connec- 
tions see  Yig.  58. 


Fio.  58. 


The  total  resistance  AD  coiisists  of  a  stretched  wire  AB, 
with  sliding  contact  at  (^,  and  ii  resistance-box  BD,  with  the 
small  resistances  towani  the  end  />. 

//,  is  a  standard  (!ell  connectod  tlirough  the  key  A' to  a 
li.xed  point  C  l»y  means  of  a  travellinjr  plug  on  the  box. 

P  and  Z-*,  are  the  terniinals  of  the  niilli-volt  meter,  //,  the 
battery  producing  its  deflections.  A'  a  resistunce  in  the  circuit 
for  varying  the  detiections,  ivnd  C,  the  coil  of  the  instrument. 

A'  and  A',  are  kept  continnou.Nly  balanced  again.st  each 
other,  so  that  the  milli-volt  meter  is  culibrated  against  the 
standard  cell.  Hence  the  resistance  AC  must  be  substituted 
for  A /J  in  (1). 


to 


(■  i 


2t?2 


LABOUA  Ton  Y  PHYSICS. 


The  resistancea  in  the  various  parts  of  the  svstom  will  dc- 
l)enil  on  the  instrument  to  l»e  c'alil)rute(i.  It  is  convenient 
to  adjust  the  resistance  l>et\veen  Ji  and  T  so  that  a  niilli-volt 
corresponds  to  a  definite  leni;tli  of  tlie  wire  .1  //. 

Vov  exanjple,  if  the  instrument  to  he  nilihrated  lu^  a 
Weston  niiUi-volt  meter  with  a  ran<;e  of  10  milli-volts,  tlu' 
wire  Ali  may  conveniently  he  a  1*.  A.  hrid^e  wire  ol 
approximately  one  ohm  resistance,  and  />  6' adjusted  so  that  a 
milli-volt  corresponds  to  ten  centimetres  of  the  hrid<;e  wire. 

The  value  of  the  resistance  to  he  unplnjijjed  hetween  It 
and  C  in  this  case  is  at  once  determined  from  the  relation 


■ ;     -  "-J 

I?   '  -i 


.001  _  .1  X  r 


where  1.434  is  the  E.M.F.  of  the  standard  cell,  /•  the  resist- 
ance of  the  whole  wire  ABy  assumed  to  he  a  metre  in 
len<rth,  and  •<•  the  unknown  resistance. 


:--t 


IJence 


X  =  142.4  X  r. 


If,  tlierofore,  hetween  /i  and  C  142  or  143  ohms  he  nn- 
i)luirircd.  each  milli-volt  will  approximately  corresp(^nd  to  ten 
centimetres  of  the  wire,  and  the  reading  can  he  taken  if  neces- 
sary to  , ,',  I,  of  a  milli  vo^^ 

Hence,  iiieastire  the  rtsi>taiU'C  of  .1 />. 

Calculate  the  approximate  value  of  ,/■. 

Tiipluj^   resistances   l.etweeu    ('  and    /^   until    on    closing.' 

A' ri<>  deflecti'iii  f»f  tin   iralvaiioiiu'ter  is  ohtaiiied. 

„ 1... ..,...: 


r» 1    n     .: 

ij   asm    li     ciiii; 


....1 !! 


Ijii-Kh- 


MJevrHICJTY. 


2(5:5 


Adjust  H  until  a  dedection  of  one  millivolt  is  obtained, 
denoting  the  deflection  by  tf. 

/*•  can  usually  be  adjusted  to  give  exact  niilli-volt  read- 
ings. 

Adjust  the  sliding  contact,  Q,  until  no  deflection  of  tin* 
galvanometer  is  obtained. 

Test  the  balance  of  A\  and  Ji  l>efore  and  after  the  obfetr- 
vation,  adjusting  always  between  C'and  IJ. 

liecord  the  position  of  Q,  and  the  reading  on  the  iuotru- 
mcni. 

Kepeat  the  observations  for  a  nuniluT  uf  points  up  the 

scale. 

If  a  Clark  cell  Ik;  used,  take  its  temperature  and  correct 
itB  E.M.F.  from  the  e<iuation 

£,  =  1.434  -  .0012(r  -  1.-.).   .     .     .       -' 


Calculate  the  vahie  T'rorrcspoiidiMg  to  eadi  rt-udiiiL'  fr<>iii 


equation 


,,     i  1.434  -  .0(»i2(r  -  \r,):A(^  /  ,■ 


Precautions.— Do  not  short-circuit  the  staiirlard  fell. 

Before  connecting  R  to  the  battery  and  niilli  volt  im  rr. 
unplug  at  least  100  ohms. 

Connect  the  negative  poles  of  the  batte^it■^  tu  the  >an)e 
end  of  the  p<jtentiometer  wire. 


i 


2rtt 


LABOR ATORT  PHYSICS. 


Example. — Enter  results  tlius : 

WESTON  MILLIVOLT  METER.    lO-MILLI-VOLT  RANGE. 
Teiiip.  of  Clurk  cell  16.5.     E,  =  1.482.     r  =  .90  ohms. 


AQ 

< 

niilli-volts. 

S-v 

10. 

1.00 

.915 

.085 

21. 

2.00 

1.93 

.07 

81.6 

8.00 

2.89 

.11 

42.0 

4.00 

8.84 

.16 

53.8 

5.00 

4.78 

.22 

•3.'.^ 

600 

6.78 

.22 

78.9 

7.00 

6.76 

.24 

84.5 

8.00 

7.73 

.27 

95  6 

9  10 

8.75 

.25 

■1 


A<^ 


HI  (Oil:  tit  ht'  JfUcd  In  1)1/  fitinfent. 


Plot  u  ciiive  foi  6  aud  6  —  v. 


iff 


BLBCrmVITY. 


2('>5 


79.  TO   DETERMINE  THE   LOGARITHMIC    DECREMENT 
OF  A  BALLISTIC  GALVANOMETER. 


References.— Hastings  and  T^each,  p.  420;  Barker,  p. 
780 ;  S.  Thompson,  p.  207. 

Apparatus  Required.— A  ballistic  galvanometer ;  a  damp- 
ing-coil; a  battery;  a  contact-key. 

Theory  of  Experiment The  ballistic  galvanometer  is  an 

instrument  for  measuring  currents  of  very  short  duration. 
The  needle  is  long  and  heavy,  so  that  its  time  of  vibration  is 
very  large,  the  time  of  the  passage  of  the  transient  current 
being  assumed  so  short  that  the  needle  remains  at  rest  during 

its  passage. 

In  making  measurements  depending  on  such  currents  the 
swing  of  the  needle  and  not  the  permanent  deflection  is  observed, 
and  iience  it  is  necessary  to  consider  how  much  the  amplitude 
of  the  vibration  of  the  needle  is  affected  by  the  damping  due 
to  resistance  of  the  air  and  other  causes.  In  a  ballistic  gal- 
vanometer, the  needle  being  heavy,  the  damping  is  usually 

very  small. 

It  may  Ik*  demonstrated  mathematically  or  shown  experi- 
mentaily  that  the  effect  of  damping  is  to  diminish  the  ampli- 
tudes of  the  successive  vibrations  in  a  fixed  proportion.  Thus 
if  a  </,,  «,,...  a„  be  the  successive  amplitudes  of  vibration 
of  a  needle,  then 


«, 


=  r. 


2ti6 


and  hence 


LAbOJiATOHY  PUrsiVH. 


a. 


(1) 


Hence 


log*  «.  -  log,  a>  =  (n  -  1)  log,  r, 


or 


log.  a,  -  log,  a^=:{n-  1)X, 


where 


^  =  log,  r. 


Hence 


^  =  7T~_n  ^'^'K*  **'  -  !<*&•  «»)•    •     •     •     (2) 


The  value  A  is  culled  the  logarithDiic  decrement. 

We  will  now  show  that  the  effect  of  dumping  on  the  anipli- 

tnde  of  any  swing  u  to  diniitjish  it  by  7.. 

Suppose  the  galvanometer  needle  to  he  set  swinging  and 
the  amplitude  of  the  first  swing  to  be  /. 

This  amplitude  is  shorter  than  the  true  amplitude,  since 
the  needle  has  been  diuujwd  through  a  half  swing. 

Denoting  by  /,  the  true  swing,  that  is,  the  nwing  that 
would  liave  been  observed  had  no  damping  been  present,  then, 
from  (2), 


A  =  -(log,  /.  -  log,  l\ 


and  hence     ^\  =  loge  /,  —  log,  l^ 


or 


lo-  /.  =  iA    I   lug,  L 


Kl.KiTlULTlY. 


267 


lleuce       /=t'^ +  '»«.' 


=  e 


X  e^J 


=  e  *'.  I 


—  M 1  _j_  -  j,  if  the  damping  be  small. 

Hence  if  the  obstTvt'd  first  swing  of  a  galvanometer  be  I, 
the  true  swing  is  given  bv  tlie  eciuation 


/.  -=  /(l  4-  I)- 


(3) 


Practical  Directions.— Set  the  galvanometer  so  that  the 
needle  swings  freely,  and  adjust  the  lamp  and  scale  until  the 
spot  of  light  is  in  focus  on  the  scale. 

('onnect  the  damiting-coil  and  battery  through  the  contact- 
kev,  and  place  the  coil  close  to  the  coil  <»f  the  giilvanonutcr. 
I?v  tapping  the  key  the  action  of  the  current  in  the  damping- 
coil  will  set  the  galviinometer-needlc  swinging.  A  little  prac- 
tice with  this  coil  will  enable  the  student  to  bring  the  swing- 
ing needle  quickly  to  rest. 

Set  the  needle  swinging  through  about  300  8cale-divi>ions, 
and  observe  the  turning-point  of  the  spot  of  light  on  the  >eale, 
following  it  as  it  swings,  and  again  reading  its  turning-point  on 
the  opposite  side  of  the  scale. 

Count  from  oO  to  oO  complete  \  il»ratioiis,  takuig  again  the 
turning- [loint  at  the  beginning  and  end  ot  tlie  last  swing. 


MICROCOPY   RESOIUTION   TBT  CHART 

(ANSI  and  ISO  TEST  CHART  No.  2) 


1.0 


I.I 


1.25 


1^1 

Hi    I 
US     I 

u 

»«•  « 


|Z8 

IIA 


III 


§23 
■■■ 

2.2 
2.0 

1.8 


^  /IPPLIED  IN/MGE    Inc 

5^  1653  Easl  Moin  Street 

r-S  Pochejler.    Ne«   York         14609       USA 

j:a  (716)   482  -  0300  -  Phone 

^B  (716)   288  -  5989  -  Fa« 


f<l  ^1 


,  ) 


268 


LABORATORY  PUTSICa. 


It- 


r 


i 


I  1 


The  sum  of  the  first  two  readings  gives  the  first  swing;  the 
sum  of  the  last  two  readings  gives  tlie  last  swing. 

Calculate  \  from  equation  (2),  multiplying  the  common 
logarithms  by  2.3026,  the  modulus  of. reduction  to  the  base  e. 

Bepeat  tlie  observations,  taking  mean  value  for  A. 

Now,  without  altering  the  control  magnets,  take  carefully 
the  time  of  20  complete  vibrations  and  thus  obtain  Ty  the 
periodic  time  of  the  needle. 

Alter  the  sensitiveness  of  the  galvanometer  by  changing 
the  position  of  the  control  magnets,  and  repeat  the  observations 
for  A.  and  T. 

Repeat  the  whole  set  of  observations  several  times,  chang- 
ing tlie  position  of  the  control  magnets  each  time. 

Plot  a  curve  with  values  of  T  for  abscissas  and  the  cor- 
responding values  of  A,  for  ordinates. 

The  value  of  X  for  any  given  sensitiveness  as  defined  by 
the  periodic  time  can  now  be  obtained  from  the  curve. 

Example. — Enter  results  thus : 


First  Swing. 

Last  Swing:. 

Number  of 
Swings. 

T 

K 

352.5 
328.5 
851.0 
847.0 
820.0 

164  5 
170.5 
210.0 
217.0 
220.0 

5U 
50 
50 
50 
50 

6.3 
5.8 
4.3 
8.9 
3.3 

.0155 
.0134 
.0108 
.0096 
.00765 

Blank  to  he  filled  in  hy  student. 


First  Swing. 

Last  Swing. 

Number  of 
Swings. 

r 

A 

t     i 


6».-Ti;«e«a?« 


i«-T::*'>'v»'Sf.'!6:a«-'.'  . 


ELECTRICITT. 


269 


80.  TO  DETERMINE  THE  ABSOLUTE    CAPACITY  OF  A 
CONDENSER  BY  A  BALLISTIC  GALVANOMETER. 

References.— S.  Thompson,  p.  425;  Uarker,  p.  662; 
Ames,  pp.  294-303;  Carhart,  pt.  11.  pp.  201-21(1;  Anthony 
and  Brackett,  pp.  291-295;  Nichols  and  Franklin,  pp.  65- 
67 ;  Hastings  and  Beach,  p.  339 ;  Watson,  p.  643 ;  Knott, 
pt.  u,  p.  136. 

Apparatus  Required. — A  ballistic  galvanometer ;  a  conden- 
ser the  capacity  of  which  is  to  be  determined ;  a  resistance- bux 
for  shunting  the  galvanometer;  a  large  resistance;  several 
batteries;  one  tapping  contact-key;  three  contact-keys  that 
can  be  permanently  closed. 

Theory  of  Experiment. — The  capacity  of  a  condenser  is 
the  ratio  of  the  charge  recpiired  to  produce  a  certain  difference 
of  potential  betv/een  its  plates  to  the  potential. 

If  C  be  the  capacity,  Q  the  charge,  and  V  the  difference  of 
potential  between  the  plates, 

V     —       y. 

Suppose  the  condenser  to  be  charged  with  a  potential  V 
through  a  ballistic  galvanometer,  in  which  case  all  the  charge 
may  be  considered  as  having  passed  through  the  coils  before 
the  needle  began  to  move, 

Then  if  G  he  the  galvanometer  constant,  3f  the  magnetic 
moment  of  the  magnet,  the  total  impulse  on  the  needle  is 

MGQ. 

If  Gj  be  the  angular  velocity  with  wliieh  the  needle  begins 


1 1 


fp:»3Ki«mrr^^«r£ 


S.«?!yv»J>Jk»ft 


.♦     !■ 


270 


LABORATORY  PHYSICS. 


to  move  and  /  be  its  inoiiient  of  inertia,  then  Ico,  the  moment 
of  momentum,  is  equal  to  the  impulse  communicated  by  the 
charge. 

Hence  /co  =  MGQ (1) 

Now  suppose  the  original  position  of  the   needle  to  be 
ABf  and  CJJ  the  pot. ion  at  the  end  of  a  swing,  a  being 


Pio.  59. 

the  angle  through  which  the  needle  swings.  Then  the  total 
displacement  of  the  north  pole  is  AP,  and  of  the  south  polo 
BR,  and  the  work  done  against  the  earth's  magnetic  field 
to  produce  this  displacement  is  given  by  the  equation 

W  =  mn{AP  +  PB\ 

where  J^is  the  earth's  horizontal  component  and  m  the  strength 
of  one  pole.     Ilo^ice 

W  =  2Ifml{l  —  cos  it) 

=     //J/(l  -  cos«) 


a 


=  2/O/sin'-.  . 


(2) 


But  the  work  done  is  also  equal  to  the  kinetic  energy  of 
the  needle. 


Hence 


a 


^  231/1  mi' ~ 
2 


(^) 


'^;*^ 


'^jms^.-M9.rwk    f^^iiS^ff -wtc' 


r.^iu.'iifiiH':?  ^^r.' 


ELECTRICITT. 


271 


Equating  the  values  of  a>  found  from  (1)  and  (3)  and  soh 
ing  for  Q,  we  obtain 


a 


2  sin  TT 


Q  = 


2  j  7// 


G 


X 


^ 


M 


(^) 


If  T  be  the  time  of  a  complete  oscillation  of  the  needle, 


and  tlierefore 


M 


fi.r 


4t' 


(5) 


Substituting  in  (4), 


n        Til   .     a 
^  =  1^«^"2' 


H 


or,  since  ^  =  7f,  the  reduction  factor  of  the  galvanometer, 


Q  = 


n 


(6) 


a 


Hence 


V  —   -^  —  ^j. — 

\  nV 


(7) 


If  now  the  same  potential  difference  be  connected  to  the 
galvanometer  terminals  through  a  resistance  jR,  the  galva- 


'B^r^EV  *  riffs^asviRi.^j^'v 


i 

I 


I!  .' 


U  ■  iS,' 


V.      ' 


;il  i 


272  LAUOliATOItY  PHYSICS. 

nometer  being  shunted  with  a  resistance  S,  the  current  through 
the  galvanometer  is  given  by  the  equation 

V  s 


Y  = 


Ii  + 


GS 

G+  8 

VS 


X 


G  +  S 


-^  =  K  tan  dj 


or 

and  hence 


^0  +  S)  +  GS 


,-„=  Ktmd, 


^ 


pl^T^ST+G-Sf  i  tan  d' 

Substituting  in  (7), 

TS  sin  i« 

;rKG!-h  ^')iif  +  G^A^i  tan  ^ 


G  = 


(8) 


(9) 


In  the  above  we  have  supposed  that  no  damping  was 
present  when  the  needle  was  displaced  by  the  charge,  and 
hence  for  sin  ^a  we  must  write 


and  (9)  becomes 


0  = 


(l  +  2)  sin  ia, 

TS  (1  +  ^]  sin  i« 

n\{G  +  S'jIiT'(^  Ha^^' 


(; 


All  the  quantities  on  the  right-hand  side  of  (10)  can  be 
observed  and  hence  C  determined. 

In  this  and  other  experiments  on  condensers  the  observa- 
tions are  taken  when  the  coiiden.ser  is  charged  through  the  gal- 
vanometer, tlins  obtaininir  the  hitstantaneonH  capaniy.  The 
value  obtained  will  usually  differ  from  that  obtained  on  dis- 
charge,  the  difference  being  due  to  absorptio  i. 


Ill 


"-W  i 


•^^vrzr^sssffMi' 


«''Bt)LV-'£t 


■ia5iis»E-.':j?> 


ELSCTBIUITT. 


273 


Practical  Directions. — A  simple  and  convenient  way  of 
connecting  the  apparatus  so  as  to  enable  the  observer  to  take 
the  two  sets  of  observations  in  rapid  succession  is  shown  in 


Fig.  60. 


Fio.  60. 

AB  is  the  condenser,  B,  the  source  of  E.^f.F.,  K  a  tap- 
ping  eontact-key,  q,  r,  and  p  plug  contact-keys,  S  the  shunt, 
and  li  a  large  resistance.  If  the  condenser  be  provided  with 
a  discharging-plug,  as  is  usual,  q  will  not  be  necessary.  If 
y,  r,  and  p  be  left  open  and  K  closed  with  a  quick  tap,  the 
condenser  will  be  charged  through  the  galvanometer. 

Closing  q  discharges  the  condenser,  closing  p  shunts  the 
galvanometer,  closing  r  brings  in  the  large  resistance  I^,  and 
the  observations  for  the  steady  current  can  be  made. 

A  few  preliminary  trials  will  first  be  necessary  to  deter- 
mine the  number  of  batteries  to  be  used  to  give  a  suitable 
throw  of  the  needle.  B  and  S  should  also  be  adjusted  in  a 
preliminary  trial  to  obtain  a  suitable  deflection. 

All  the  connecting  wires  should  be  carefully  insulated  to 
prevent  leakage. 

Brint'  the  needle  to  rest  by  means  of  the  damping-coil. 

Close  /rwith  a  sudden  tap,  freeing  it  as  quickly  as  pos- 
sible  and  observe  the  throw  of  the  needle. 

Kepeat  the  observations  several  times,  taking  the  mean 
throw. 


fjS&jTr«c>->-'<WS'-f'?y^.^.iiF3ggfr»Bf  >  /Mg~ 


y:s^i^!>-2::ssB3m^  "ss'  msmxa^at:  ^ 


I  il 
1 


'I 

V 


I  'I 
ill 


;ji 


1 1 

it 


274  LABORATORY  PHTSIC8. 

Close  the  keys^,  j^,  r,  and  obaeive  the  deflection. 
Read  R,  S^  and  tf. 

throw 
Calculate  sin  for,  knowing  that  tan  2a  = 


Calculate  tan  6*,  knowing  that  tan  2^  = 


scale  distance' 
scale  distance* 


If  the  throw  and  deflection  be  both  small  and  the  scale 
di-stance  of  the  galvanometer  large,  it  will  usually  be  suffi- 
cient to  substitute  for  sin  ^a  one-half  the  throw  of  the  needle, 
and  for  tan  6  the  deflection. 

Repeat  the  observations. 

Take  the  time  of  50  swings  of  the  needle,  and  calculate 
jT,  the  time  of  a  complete  oscillation. 

A  can  be  obtained  from  the  curve  for  the  logarithmic 
decrement  by  means  of  T  if  the  galvanometer  be  the  one 
nsed  in  the  last  experiment,  otlierwise  \  must  be  obtained 
directly. 

In  the  example  given  below  6  storage  cells  were  used. 

Example, — Enter  results  thus : 

N ALDER  i  MICRO-FAB A.D  No.  347f. 


Throw. 

R 

S 

i 

T 

A 
2 

C 

104 
106 

1000 

(i 

■ 

184.7 
185  0 

8".0 

.006 

.333 

Bla 

nk  to  he  filled  in 

hy  stude 

nt. 

Throw 

R 

s 

i 

T 

K 

2 

C 

J 

ELECrmCITT. 


275 


8i .  TO  COMPARE  THE  CAPACITIES  OF  TWO  CONDENSERS. 
DIRECT-DEFLECTION  METHOD. 

References. — As  in  last  exj>eriinent. 

Apparatus  Required. — A  cttiulentjer  whoso  capacity  lias 
been  determined ;  CDndeiisers  for  coinparison ;  a  ballistic 
galvanometer ;  several  batteries ;  a  Fold  commutator ;  a  con- 
tact-key. 

Theory  of  Experiment. — If  a  condenser  be  charged  to  a 
potential  v  through  a  ballistic  galvanometer,  we  Lave  from 
equation  (7)  of  tlie  last  experiment  the  relation 


C  = 


KT 

nv 


a 


0) 


the  terms  having  the  same  meaning  as  in  that  case. 

Similarly  if  a  second  condenser  be  charged  with  the  same 
potential, 


Hence 


KT 

a 

t\ 

nv 
sin 

sm 

2 

c\ 

2 

c 

sin 

• 

a 

1 

{^ 


.     .     (3) 


If  observations  for  a  and  a,  be  made,  C,  can  be  calculated 
if  C  be  known. 


__ 


sxr^'^iar^  Vh^  7-  csStasu'x^  y„ijah 


sir£  ..'^'^ts^tfTB.:  .Biia'Zi^?7.^Hbrta!^'.£::«<.?:i;^iiBa&MLau  .02:.. 


Ill 

a  1 


.'1 


%  I 


276 


LABOHATOJir  PIIT81CS. 


Practical  Dlrectiona.— A  convenient  method  of  making 
tl»e  connections  is  shown  in  Fig.  CI. 

AB  and  CD  are  the  two  condensers,  abcdef  a  1  ohl 
commutator  with  the  connectors  on  the  base  removed,  B, 
the  source  of  E.M.F.,  A'  a  contact-key. 

Tlie  battery  and  <?iilvanoineter  are  connected  to  the 
contacts   in  which  the  rocker  dips.     On  rocking   the  com- 


mutator toward  AB,  ae  and  J/ are  connected,  and  on  closing 
K  the  condenser  AB  is  charged  through  the  galvanometer. 
On  rocking  toward  CD  the  same  thing  occurs  for  the  con- 

denser  CD.  •       -c 

The  observations  can  then  be  taken  in  rapid  succession,  if 

the  galvanometer  needle  be  brought  to  rest  with  a  dampmg- 

'''''  The  condensers  must  be  discharged  after  each  observation. 
If  they  are  not  supplied  with  plugs  for  the  purpose,  they 
can  be  short-circuited  through  the  points  in  which  they  make 
contact  with  the  Pohl  commutator.  If  the  battery  be  con- 
nected directly  through  A' to  /,  and  the  galvanometer  to  the 
rocker  terminals  of  another  Pohl  commutator  with  base  con- 
nectors removed,  the  other  ternnnals  being  connected  m  pairs 
to  ah  and  cd,  then  the  condensers  can  be  charged  by  rock- 
ij,g  the  first  and  closing  K,  and  discharged  through  the  gal- 


'imi^SW^SK'. 


ELECTRICITT. 


277 


vanoineter  by  rocking  the  second  commutator,  thus  giving  a 
conipuriBon  on  discharge.  Compare  the  several  condensers 
given  with  the  standard. 

If  the  galvanometer-throws  be  nearly  equal,  they  may  be 

substituted  for  sin  ^  and  sin  ~  in  equation  (3),  otherwise 
sin  ~  and  sin  -^  must  be  calculated. 
Example. — Enter  results  thus : 


Condenser. 

Throw. 

Scale  DtsUnce. 

-n-- 

C 

Staudard 

iM.F 

.2M.F 

.5M.  F 

225 

142.8 

825 

1  Meter 

.382 
.210 
.495 

Blank  to  he  filled  in  hy  student. 


Condenser. 

Throw. 

Scale  Distance. 

sin" 

r 


278 


LABORATORY  PHYSICS. 


illl 


','i' 


I 

III 


\  U 


82.    TO   COMPARE    THE    CAPACITY    OF    CONDENSERS. 
METHOD  OF  MIXTURES. 

References. — A«  in  Experimeiit  7'J. 

Apparatus  Required.— A  KoiiHitivc  retioctin^  galvanom- 
eter; two  reftistunee-boxei* ;  two  i'ohl  coinniututorH;  a 
contact-key;  pevoral  l»i\tterics. 

Theory  of  Experiment.— In  tliis  method  the  condensers  are 
charged  so  tliat  tlie  two  charges  are  equal,  the  potentials 
producing  them  being  uneciual. 


Since 


n  — 


and 


then 


0) 


If  the  condensers  he  chargetl  iiiid  the  charges  allowed  to 
mix  in  such  a  way  as  to  neutralize  each  other,  the  system 

being  then  discharged 
through  a  galvanometer, 
the  chiirgos  are  e<iuiil  if 
no  detiection  is  obtained. 

Practical  Directions. 
— The  connections  can  be 
made  as  in  Fig.  <>2. 

Ali  and  CI)  are  the 
two  condensers,  li  and 
Ji^  two  resistance-boxes 
connected  tothe  terminals 
of  a  battery  -/>,,  (f,  h,  <*, 
flr,,  J,,  e,,  tlie  terminals 


M 


3ZIJ 


Hllll'illlllF 

B, 


Fio.  62. 

of  a  Pohl  commutator  from  which  the  base  connectors  have 
been  removed. 

By  rocking  the  switch  so  as  to  connect  h,  to  r,,  and  h  to  c, 
the  two  condensers  will  bo  charged  with  potentials  propor- 
tional to  R  and  R,^  so  that 


ELECTRICITY. 


279 


A*  _  r 
Ji\-  \\' 

By  rocking  the  switch  8c»  as  to  connect  a,  to  ft,,  uiul  a  to  A, 
tlie  battery  is  thrown  out  of  the  circuit  ami  the  chur},a'»  on 
the  two  condenisers  neutralize  each  other,  the  nepitive  phites 
of  tlie  one  beinj<  connected  to  the  jwsitive  plates  t»f  the  other. 

If  the  charges  are  equal,  a  complete  neutralization  tukis 
place.  If  not,  the  two  make  one  coiulenser  syKteni  char^td 
with  the  ditTerence  between  the  two  charges,  and  on  closing  K 
a  discharge  will  take  place  through  the  galvanometer. 

If  an  approximate  relation  between  C  and  C\  be  known, 
H  and  I(,  can  be  roughly  adjusted.  Otlierwise  their  values 
can  only  be  determined  by  trial. 

Repeat  the  adjustment  until  no  deflection  is  obtained. 

Between  the  trials  the  condensers  should  be  thoroughly 
discharged.  This  can  be  done  by  keeping  A'  closed  for  a  few 
seconds  after  each  discharge. 

Record  the  values  of  H  and  i?,. 

Compare  the  condensers  given  with  the  standard,  and 
calculate  their  values  in  each  case. 

Example. — Enter  results  thus : 


Cot.'euser. 

R 

Ri 

C 

^' 

Standard 

JM.F 

.2M.F 

.6BLF. 

2000 

3400 
1295 

.832 

.lft5  M.  F. 
.490 

1 

Blank  to  he  filed  in  hy  at  x  dent. 


CondenBer. 


Bi 


C, 


I 


280 


LABORATORY  VtiYSlCa. 


;1 

H: 


* 

^ 


.t 


83.  TO    COMPARE  THE  CAPACITIES   OF  CONDENSERS. 

BRIDGE  METHOD. 

References. — As  in  Experiment  79. 

Apparatus  Required. — As  in  the  last  experiment. 

Theory  of  Experiment. — In  the  last  experiment  the  charges 
were  equal  and  the  potentials  unequal ;  in  this  experiment  the 
potentials  are  equal  and  the  charges  unequal.     Suppose  the 


Fig.  68. 

two  condensers  and  the  two  resistances  connected  in  the  arms 
of  a  "Wheatstone  bridge,  Fig  63,  C  and  C,  being  the  conden- 
sers, R  and  iJ^Jlhe  two  resistances. 

In  order  that  no  current  flow  through  the  galvanometer 
on  charging  the  condensers,  that  is,  on  closing  A",  L  and  M 
must  be  at  the  same  potential. 

Denote  tlie  common  potential  of  Z  and  Mhy  Fand  the 
potential  of  A  by  F,. 

The  total  quantity  of  electricity  which  flows  into  C  is 
therefore  give  by  the  relation 


(V,  —V\ 

Q  =zyt  =    \  -^-g jt,       .... 


(1) 


!-•>.«■•>- -iSJ^-W  't  ■ 


ELECTRICITY. 


2«1 


where  y  is  the  current  and  t  the  short  tune  required  to  charge 
the  condenser. 

Similarly  the  relation  for  C,  is 


Hence,  from  (1)  and  (2), 


(2) 


(3) 


But 


Q 


Q, 


C=y,  and   C;=y, 


the  potentials  being  the  same  on  the  plates. 

Hence  £  ~  ^-  ^ 

lience  C,~  Q,~  H' 


or 


(4) 


If,  therefore,  ^and  R^  be  adjusted  so  that  m  charging  the 
condensers  no  deflection  of  the  galvanometer  is  obtained,  C,  can 
be  calculated  from  (4),  C  being  known. 

Practical  Directions. — The  connections  can  be  made  exactly 
as  in  Fig.  63. 

Be  careful  to  insulate  all  the  parts  of  the  apparatus. 

Adjust  R  and  E^  until  no  deflection  is  obtained  on  clos- 
ing JT. 

Between  the  trials  the  condensers  must  be  discharged  com- 
pletely. 


282 


LABORATORY  PHYSICS. 


Ji  and  Ji^  sliould  bo  as  large  us  possible. 
A  ballistic  galvanunictcr  iei  nut  necessary ;    any  sensitive 
galvanometer  will  serve  the  purjwse. 

Conipure  the  coudensei*s  as  in  previous  experiments. 

Example. — Enter  results  thus : 


• 

Condenser. 

R 

Ki 

c 

c, 

Standard 

iM.  F 

.2M.  F 

.5M.  F 

2000 

3400 
1^96 

.882 

.195 
.490 

Blank  to  hefilUd  in  hy  stttdent. 


Condenser. 

R 

R, 

C 

c, 

a 


; 


I 


84.  MEASUREMENT  OF  E.M  F.  AND  BATTERY  RESIST- 
ANCE BY  CONDENSER  METHOD. 

References. — S.  Thompson,  p.  422. 

Apparatus  Required. — A  condenser;  a  ballistic  galva- 
nometer; a  resistance-box;  a  contact-key;  batteries  for 
measnrement. 


ELECTRICITY. 


283 


Theory  of  Experiment. — (1)  If  a  coiideiiKcr  of  capacity  C  be 
cliari^ed,  by  means  of  a  battery,  with  E.M.K.  7i',  we  Jiave  the 
relation  (see  (7)  page  27 Ij 

CE=  K.mxU (I^ 

If  the  same  condenser  be  charged  with  an  E.M.F.  h\, 


CE,  =  K,  Bin  Ja.. 


Hence 


E  _  sin  ^a   _  <5 

E^  ~  sin  ia,  ~  ^^  ' 


(2) 
(3) 


approximately,  where  6  and  (J,  are  the  galvanometer  thrown 
in  the  two  cases, 

"With  a   standard  condentier  the    iiJ(.tho<l   U   suitable  for 
comparing  the  electromotive  forcen  of  batterieB. 

(2)  "We  have  for  a  battery   cliarging   the  condenser  the 
relation 

CE  =  Kd. 

If  now  the  battery  be  shunted  witli  a  shunt  S  and  the  con- 
denser charged,  we  have  the  relation 


Hence 


or 


V 

S 

—  K 

^^  B 

+  s 

B  ^ 

s 

P  - 

S(6 

-_A) 

<y. 


r4) 


from  which  the  batterv  resi-taTifp  li  can  be  calculated. 

Practical  Directions. —  !•  rMrjr,<-ct  iu  mtjck  a  Clark  cell, 
tlie  sralvanometer.  and  the  coiidfn-cr  rhro'iirb  a  cftntaft-lrfv, 
Tht'  T'lark  cell  f^liould  be  coTincftfl  in  '.v  irii-aiiK  of  a  tliref-wav 
kev  iu  addition  to  the  contact  k'v.  tluif-  allowing  it  to  remain 


28+ 


LABORATORY  PHYSICS. 


i 


}  IS 
t  ■  - 


purinatfently  in  the  connections,  while  anotlier  battery  to  bo 
compared  with  it  can  be  alfio  connected  and  each  nsed  in  turn 
by  simply  altering  the  jlng  in  the  three-way  key.  Observe 
the  throw  for  each  of  the  two  batteries  in  snccession,  <^  and 
d,,  and  also  the  throw  for  each  shunted. 

Close  the  shunt  through  a  contact-key  pressing  the  key 
only  for  the  moment  necessary  to  make  the  observation. 

Special  care  nmst  be  taken  not  to  short-circuit  the  Clark 
cell,  as  it  polarizes  very  rapidly. 

Read  the  temperature,  t,  of  the  Clark  cell. 

Assuming  the  E.M.F.  of  the  Clark  cell  to  b6 

1.434  -  .0012(<  -  16), 

calculate  the  electromotive  forces  of  the  others. 
Calculate  their  resistances  from  equation  (4). 
Example. — Enter  results  thus : 

Tempeiature  of  C.  C.  16.5 


Battery. 

6 

1 

B 

Clark  cell 

65               80       i        40 

1.482 
1.85 
2.81 
1.07 

60. 
2.2 
0.8 
4.6 

Leclancbt' 

61               10       '        50 

Storege-batterv 

Daniell ". 

105 
49 

10 
50 

97 
45 

Blank  to  he jt'hd  tu  hy  student. 


Battery. 

< 

S 

«. 

E 

B 

iAL'^«^  ^-k «[-%«» .^vfi^cr-  msji  inTr  i/"i  'mwn  «iv^i^s 


INDEX. 


Absolute  Capacity  of  a  Condenser 269 

Air-tberiuoraeter,  Constant  Volume l'>6 

Constant  Pressure lUJ 

Ammeter,  Calibration  of,  by  Gas  Volumeter 235 

by  Siemens  Electro-dynamometer 241 

B.  A.  Bridge 1«2 

Ballistic  Galvanometer,  Log.  Dec.  of 265 

Capacity  of  Condenser  by 270 

Batteries,  Resistance  of,  by  WLeatt-tone's  Bridge IVIJ 

by  Condenser  Meiho<J 284 

E.  M.  F.  of  Condenser  Meth<^ 2Hi 

Bridge- wire.  Calibration  of 214 

Calibration  of  BrMge-wire 214 

Ammeter '■ 2ii5,  xi41 

Millivolt  Meter 261 

Capacity  f.f  a  Confieuser,  Absolute 270 

Coefficient  of  Kipaision  of  Air 106 

Increase  of  Pressure US 

Ex pausion  of  G lycerine 1  'K) 

of  Brass 108 

Compass- lx)x  Variometer 1  '"'^ 

Condenser,  Absrjiute  Capacity  of "-^0 

CompariM)n  of  rapaciti.-(;  of ?"6,  -7^'.  2>*(i 

E.M.F.  of  Batteries  by '■i>^^^ 

C-oDcave  Lens,  F^  >c«  1  Len^rtL  of 70.  7:j 

Convex  I^ens,  Focal  Leii>rtL  of 60,  tii),  Go   6H 

Coulomb  Balance   H:^. 

Current.  Absolute  Measure  of 168 

Curvature  nf  Spberica!  Surface  . .    Jil 

by  Spiieroiiieter    51 

by  Kellec:  tou   .  .    54,  57 

385 


286 


INDEX. 


PAOI 

D'Arsonval  Qalvanometer,  Resistance  of 243 

Constant  of 247 

CalibratioQ  of  Scale  of 251 

Measurement  of  Potential  by 25,  51 

Earth's  Magnetic  Field,  Intensity  of,  by  Magnetometer  Method  146 

by  Tangent  (ialvanometer 173 

Electromotive  Force,  Comparison  of 229,  232 

Electro-chemical  Equivalent  of  Hydrogen 166 

of  Copper ,   171 

Equivalent  Length  of  a  Magnet. 150 

Focal  Length  of  a  Convex  Lens 60,  63,  65,  68 

of  a  Concave  Lens 70,  73 

Galvanometer,  Ballistic 265 

D'Arsonval,  Ke.sistance  of 243 

ConsUnt  of 247 

Calibration  of  Scale  of 251 

Potential  Differences  by 255 

Differential    185 

Reduction  Factor  of 176 

Resistance  by  Shunting 191 

Sine  and  Tangent 159 

Glass,  Refractive  Index  of 43 

Heat,  Specific,  of  Copper  and  Zinc 117 

Latent,  of  Fusiouof  Ice 121 

of  Steam 124 

Horizontal  Component  of  Earth's  Magnetic  Field  by  Magnometer  Method  146 

by  Tangent  (ialvanometer  173 
Variation  of 155 

Index  of  Refraction  of  Glass 43 

of  Liquid 9'3 

Joule's  Law 203 

Kundt's  Tube 24 

Intent  Heat  of  Fusion  of  Ire 121 

of  Steam 124 

Light,  Comparison  of  Intensities  by  Bunsen's  Photometer  33 

by  Rum  ford's  Photometer. .    34 

Lines  of  Force,  Blue-printing 128 

Lissnjous  Figures 13 

Logarithmic  Decrement , 265 


'i* 


_'  .''''..4a1».':97w% 


INDEX. 


287 


PACK 

Magnet,  Finding  Moment  of 128,  134, 189,  148 

Equivalent  Length  of 150 

Magnetic  Field,  Mapping 129 

Intensity  of 14«.  HS 

Magnifying  Power  of  Miscroncope 77 

of  a  Telescope 81 

Melde's  Method,  Laws  of  Stretclied  Strings 22 

Microscope,  Construction  of 76 

Magnifying  Power  of ....     77 

Milli-volt  Meter,  Calibration  of  260 

Neutral  Point 129 

Organ-pipe,  Frequency  of 8 

Pendulum  chronograph 28 

Photometer,  Bunsen's 33 

Ruiiiford's 84 

Prism,  Angle  of 40,  89 

Refractive  Index  of 46,  89 

Reduction  Factor  of  a  (Jalvanometer 176 

Reflection,  Law  of 36 

Refraction,  Law  of ^3 

Refractive  Index  of  Glass 43 

of  Prism 46,  89 

of  Liquid. .. .   93 

Resistance,  Measurement  of,  liy  Tangent  Qalvanometer 179 

by  B.  A.  Bridge 182 

by  Differential  Galvanometer 185 

by  Wheatstone's  Bridge 199 

of  Qalvanometer  by  Shunting 191 

by  Wheatstone's  Bridge 199 

Comparison  of,  Carey  Foster  Method 209 

Variation  of,  with  Temperature 218 

Measurement  of  Small "'21 

of  liarge '■•*2<'> 

Sixicific 1^8 

l{esonance-tui)e * 

Siemens  Electro  dynamometer 238 

Constant  of 238 

(."a'ibration  by 241 

Siren "^ 

Sonometer ' 


if 


J 


:ii:^l 


288  INDEX. 

PAOI 

Sound,  Velocity  of,  in  Air  by  Resonwjce-tube ^ 

by  Kundt'B  Tube ^^ 

27 

in  Brass  *' 

.„    „    ,  117 

Specific  Heat 

of  Copper,  Method  of  Mixture **' 

of  Zinc j*^^ 

Kesistance 

„  08 

Spectroscope . 

Spectrometer ....... 'bVm  67 

Spherical  Surface.  Curvature  of oi. »«.  «• 

Spberoineter,  Curvature  by 

Strings,  Velocity  of  Waves  in 

75 
Telescope,  Construction  of 

Magnifyng  Power  of 

Thermometer,  Construction  of  Spirit 

Testing  Fixed  Points  of ^ 

Air.  Constant  Volume |^ 

Constant  Pressure J^^ 

„      .      _  ,  143 

Torsion  Balance 

Tuning-fork,  Frequency  of,  by  Sonometer ^ 

by  Melde's  Method ^^ 

by  Falling  Plate ^^ 

by  Pendulum-chronograph 28 

Tuning-forks,  Comparison  by  Beats 

2  23 
Vibrating  Strings,  Laws  of 

Variometer  Compass-box 

85 
Wave-length  of  Light  Vibrations ^" 

Waves,  Velocity  of 

Weight-thermometer 

Wheatstone's  Bridge 


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Practical  Farm  Drainage ""<'• 

FolweU's  Sewerage.     (Designing  and  Maintenance.) »'<>. 

FreiUg's  Architectural  Engineering,     ad  Edition.  Rewritten 8vo. 

French  end  Ives's  Stereotomy "'"' 

Goodhue's  Municipal  Improvements "f*"' 

Goodrich's  Economic  DUposal  of  Towns'  Refuse o»o> 

Gore's  Elements  of  Geodesy *'*•' 

Hayford's  Text-book  of  Geodetic  Astronomy »'°> 

Howe's  Retaining  Walls  for  Earth ^    •  ""»»• 

Johnson's  Theory  and  Practice  of  Surveying !>n»«»  »»<>• 

SUtics  by  Algebraic  and  Graphic  Methods «'<>• 

Klented's  Sewage  Dteposal •    • •  """'' 

LapUce's  Philosophical  Essay  on  Probabilitief      (Truscott  and  Emory.)  lamo, 

Mahan's  Treatise  on  Civil  Engineering.     (18      )    (Wood.) 8vo 

•       Descriptive  Geometry °^°' 

Merriman's  Elements  of  Precise  Surveyln?  and  Geodesy ovo. 

ElemenUofSaniUry  Engineering ■ ■  •  ■^''°' 

Merriman  and  Brooks'*  Handbook  for  Surveyors i6mo.  morocco. 

Rugent's  PUne  Surveying °*°' 

Ogden's  Sewer  Deslsin •  •  •  .  •  ■.,  :"^°' 

Patton's  TreatlM  on  CivU  Engineering 8vo.  half  leather, 

Reed's  Topographical  Drawing  and  Sketching 4to. 

Rideal's^ewage  and  the  BaeterUl  Purification  of  Sewage »'». 

Siebert  and  Bieein'n  Modem  Stone-cutting  and  Masonry ovo. 

Smith's  Manual  of  Topographical  Drawing.     (McMillan. ) 8vo, 


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-■^^    IS 


.onderickef.  Graphic  Sftic  with  AppUc.Mon.  to  Tr«..es.  B..m..  .nd 

.  T^ntwit^tavilKe".;-.  Poc^.t-booic .        .6»o.  .oroccc 

Waifi  Eneineering  «id  Architectural  Juritprud.nee ^^^^^ 

Law  of  Operation.  PreUminary  to  Construction  in  Engineering  "«»  Archi- 
tecture      Sheep. 

8vo, 

Law  of  Contracts g^^ 

«r-^.n>.  St»r»otomv— Problems  in  Stone-cutting 

:;:.r  SlelTthe  C.e  and  Adiust«,nt  of  --eerin.Jn^nts. 

*  Wheeler's  Elementary  Course  of  Civil  Engineering |^^- 

Wilson's  Topographic  Surveying 


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BRIDGES  AND  ROOFS. 

Boiler',  Practical  Treatise  on  the  Construction  of  Iron  Highway  Bridges  J^o.  ^^  oo 

*         Thames  River  Bridge I  _        '      a,  v,..i  Tiihc   and 

Burr's  Course  on  the  Stresses  in  Bndges  and  Roof  Trusses.  Arched  R.bs.  ar^d  ^  ^^ 

Suspension  Bridges. .  ........  ^^  .  •  • ^^  ^ 

Du  Bois's  Mechanics  of  Engineering.     Vol.  II ^^^^  ^  ^^ 

Foster's  Treatise  on  Wooden  Trestle  Bridges ^^^_  ^  ^^ 

Fowler's  Coffer-dam  Process  tor  Piers '.'.'.'..'.......  .8vo,  i  25 

Greene's  Roof  Trusses gyo^  2  50 

Bri<'ge  Trusses g,o^  ,  50 

Arches  in  Wood.  Iron,  and  Stone g^^  ^  ^^ 

Howe's  Treatise  on  Arches „, '  \.      j  c.  .1 8vo.    2  00 

Design  of  Simple  Roof-trusses  m  Wood  and  Steely        .^  •  ■    •  _^  .^ _ 

Tohnsonl^ryan.  and  Turneaure's  Theory  and  Practice  in  the  De^^^mng^of  ^^  ^ 
Modem  Framed   Structures -■■ 

Merriman  and  Jacoby's  Text-book  on  Roofs  and  Bridges:  ^^^^    ^  ^^ 

Parti.— Stresses  in  Simple  Trusses    g^^^    ^  ^^ 

Part  11. — Graphic  Statics ;  <,„„     ,  rn 

Jaruk-Bridge  Design.     4th  Edition.  Rewritten 8vo.    ^^  5° 

Part  IV.— Higher  Structures ^^^^    ^^  ^ 

Wright's  Designing  of  Draw-spans:  g^^^    ^  ^^ 

Part  I    — Plate-girder  Draws _ - 

pSlL-Riveted-truss  and  Pin-connected  Long-span  Draws.  ....   Svo.    2  50 

Tt/o  parts  in  one  volume 


(**■ 
M 


m 


.dfi 


HYDRAULICS. 

Bazin's  Experiments  upon  the  Contraction  of  the  Liquid  Vein  Issuing  from^an 

Orifice.     (Trautv-ne.) g^^^^ 

Bovey's  Treatise  on  Hydra^.ics g^^'_ 

Church's  Mechanics  of  Engineering ,_  '      r'y,.„„^,. nappr, 

Diagrams  of  Mean  Velocity  of  Water  in  Open  Channels   . . _    ^.  .^^pap  r. 
Coffin's  Graphical  Solution  of  HydrauUc  P-"e.s^^^  .  :6mo.  mo    c^o 

Flather's  Dynamometers,  and  the  Measurement  of  Power ^^^ 

Folwell's  Water-supply  Engineering g^^'_ 

Frii-ell's  Water-power 

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4  oo 

5  00 


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Fuertes's  Water  and  Public  Health ""»<>•    »  5© 

Water-filtration  Work. "mo,    a  50 

Ganguillet  and  Kutter'»  General  ForrauU  for  the  Uniform  Flow  of  Water  m 

Rivers  and  Other  Channete.     (Bering  and  Trautwine.) 8vo,    4  00 

Hazen'8  FUtration  of  PubUc  Water-supply 8vo.    3  00 

Hazlehurst's  Towers  and  Tanks  for  Water- works 8vo,    a  50 

Herschel's  115  Experiments  on  the  Carrying  Capacity  of  Large,  Riveted,  Metal 

Conduits 8'°'    '  °° 

Mason's    Water-supply.     (Considered    Principally   from   a   SaniUry   Stand- 
point.)    3d  Editioi,  Rewritten 8vo,  a  00 

Merriman's  Treatise  on  Hydraulics,     oth  Edition.  Rewritten 8vo,    5  00 

*  Michie's  Elements  of  Analytical  Mrrhanics 8vo,    4  00 

Schuyler's   Reservoirs  for  Irrigation,  Water-power,  and   Domestic   Water- 
supply ^»rK«  8vo,    5  00 

**  Thomas  and  Watt's  Improvement  of  Riyers.     (Post.,  44  c  additional),  4to,    6  00 

Turneaure  and  Russell's  PubUc  Water-suppUes 8vo.    5  00 

Wegmann's  Design  and  Construction  of  Dams. 4to,    s  00 

Water-supplyof  the  City  of  New  York  from  1658  to  183s 4to,  to  00 

Weisbach's  Hydraulics  <ind  HydrauUc  Motors.     (Du  Bois.) 8vo,    5  00 

Wilson's  Manual  of  Irrigation  Engineering Small  8vo.    4  00 

Wolff's  WindmiU  as  a  Prime  Mover 8vo,    3  00 

Wood's  Turbines *^°'    '  5o 

Elements  of  Analytical  Mechanics 8vo,    3  00 


MATERIALS  OF  jENGINEERING. 

Baker's  Treatise  on  Masonry  Construction 8vo, 

Roads  and  Pavements *'^''« 

Buck's  United  States  PubUc  Works Oblong  4to, 

Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo, 

Burr's  Elasticity  and  Resistance  of  the  Taaterials  of  Engineering.     6th  Edi- 
tion, Rewritten 8vo, 

Byrne's  Highway  Construction 8vo. 

Inspection  of  the  Materials  and  Workmanship  Employed  in  Construction. 

i6mo. 

Church's  Mechanics  of  Engineering 8vo, 

Du  Bois's  Mechanics  of  Engineering.     Vol.  I Small  4to, 

Johnson's  Materials  of  Construction Large  8vo, 

Keep's  Cast  Iron 8vo, 

Lanza's  Applied  Mechanics 8vo, 

Martens's  Handbook  on  Testing  Materials.     (Henning.)     2  vols l/o. 

Merrill's  Stones  for  Building  and  Decoration 8vo, 

Merriman's  Text-book  on  the  Mechanics  of  Materials 8vo, 

Strength  of  Materials i2mo, 

Metcalf's  SteeL     A  Manual  for  Steel-users i2mo, 

Patton's  Practical  Treatise  on  Foundations. 8vo, 

Rockwell's  Roads  and  Pavements  in  France i2mo. 

Smith's  Wire :  Its  Use  and  Manufacture Small  4to, 

Materials  of  Machines i2mo. 

Snow's  Principal  Species  of  Wood 8vo, 

Spalding's  HydrauUc  Cement i2mo, 

Text-book  on  Roads  and  Pavements i2mo, 

Thurston's  Materials  of  Engineering.     3  Parts 8vo, 

Part  I. — Non-metallic  Materials  of  Engineering  and  Metallurgy 8vo, 

Part  II.— Iron  and  Steel 8vo, 

Part  in. — A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 
Constituents 8vo, 


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erration  of  Timber g^^,^ 

ElemenU  of  Analytical  Mechanics 


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RAILWAY  EKGINEERING. 

.^    ,   »„,  Ch.«t  RaUwav  Enpneers.    3X5  inches,  morocco,    1  aS 

Andrew.'s  Handbook  for  Street  ff^^V^^^-.n.  4to.  S  00 

Berg'.  BuUding.  and  Structure,  o  A."«""°  «*"'°»*'' ,6mo.  morocco,    i  50 

Bt  .ok.'.  Handbook  of  Street  lUilroad  Location ^^^^.  ^^^^^  ^^    ^  ^^ 

Li^tt.'.  CivU  Engineer's  Field-book •  ^^^^^  ^^^     .^^    ^  ^ 

CrandaU's Tran.ition Curve •    •  •• ^vo,    i  50 

RaUway  and  Other  EwthworkTab^^^^^^  ^  ^ 

Dawwn'.  "Engineering"  and  Electric  iracuu  „     .  Paper,   5  <x> 

.oLtf,  Tuu.n...  EwWv.  CwmiK.  """^  °^'  ■•"■  c„  jbotri.       >S 

bankmsnts t^''.'      ^  i6mo,    iloo 

MoUtor  and  Beard'.  M«.«al  for  Rerident  Engineer. .^n^o'.  morocco,_aJH» 

Hagle'.  Field  Manual  for  Rai^oad  Engineers ^^^^^  moroccoTT 00 

PhUbrick'8  Field  Manual  for  Engineer.^. . . .  8vo,    a  00 

Pratt  and  Alden's  Street-raUway  Road-bed •  -^^^  „o,occo.   3  00 

Searle.'.  Field  Engineering .i6mo,  morocco,    i  50 

Railroad  SpiraL ••  •  •  •  •    •  ■  • gyo,    i  50 

Taylor's PrismoidalFomul-an^E^^^  Contentsof  Excavations  and 

•  Trautwine's  Method  of  CalcuWtmg  ine  vuu«.  ^^^^    ^  ^ 

Embanl^ents  by  the  Aid  of  ^J*^"-- ^    Curves'  for'  Railroads. 

•  The  Field  Practice  of    Laying    Out    circular  „nio,  morocco,    a  50 

Paper,        aS 

•  Cross-section  Sheet. „  .j^..'  Rewritten   .....  i6mo.  morocco.    5,00 

Webb's  Railroad  Construction.     ,^<^^^'*  '^°°;.  J'^^R^vays SmaU  8vo.*5  00 

WelUngton's  Economic  Theory  of  the  Location  of  Rai.way 


DRAWING. 

8vo,    3  50 

Barr'r  Kinematics  of  Machinery g^^^    j  00 

•  Baitlett's  Mechanical  Drawing . . .  8vo,  paper,    1  00 

CooUdge's  Manual  of  Drawing g^o^    4  00 

Durlev's  Kinematics  of  Machines _ '.  ,„,„-MivP 8vo,^  a  00 

Hill's  Text-book  on  Shades  and  Shadows,  and  1  rrspective 

Jones's  Machine  Design:  gyo^    150 

Part  I.— Kinematics  of  Machinery  ■•■.■•■/_■;,■ gvo,    3  00 

Part  n.-Form,  Strength,  and  Proportious  of  Parts ^^^^    ^^ 

MacCord's  Elements  of  Descriptive  C  omeUy ^^^^    ^  ^^ 

Kinematics;  or.  Practical  Mechanism .V.V.V.  .V.  .  .  .4to,    4  00 

Mechanical  Drawing gyo,  x  50 

Velocitv  Diagrams Rvn,    i  50 

•  Mahan's  Descriptive  Geometry  and  Stone-cUtnng ^^^^    ^  ^^ 

Industrial  Drawing.    (Thompson.). . ^^^^    ^  ^^ 

Reed's  Topographical  Drawing  and  Sketchmg 

8 


Reid's  Coune  in  Mectuinical  Drtwing '"' 

Text-book  of  Mechanical  Drawing  and  ElemenUry  Machine  Design    Bvo, 

Robinson's  Principles  of  Mechanism ^°' 

Smith's  Manual  of  Topographical  Draring.    (McMillan.) o^o- 

Warren's  Elements  of  Plane  and  SoUd  Free-hand  Geometrical  Drawing   .  umo, 

Drafting  Instruments  and  Operations lamo, 

Manual  of  Elementary  ProjecUon  Drawing. . . . ." •  ■•     """O' 

Manual  of  Elementary  Broblems  in  the  Linear  Perspective  of  Form  ana 

Shadow """'• 

Plane  Problems  in  Elementary  Geometry ""**>• 

Primary  Geometry i»mo, 

Elements  of  Descriptive  Geomtjy.  Shadows,  and  Perspective Hvo, 

General  Problems  of  Shades  and  Shadows |^°' 

Elements  of  Machine  Construction  and  Drawing °'°' 

Problems.  Theorems,  and  Examples  in  Descriptive  Geometrv 8vo. 

WeJsbach's  Kinematics  and  tiie  Power  of  Transmission.      (Hermann  and 

„,  .     X  ovo, 

Kleu.) 

Whelpley's  Practical  Instruction  in  the  Art  of  Letter  Engraving i«no, 

Wilson's  Topographic  Surveying '"' 

Free-band  Perspective '**' 

Free-hand  Lettering.     [In  preparation.)  ■ 

Woolf's  Elementary  Course  in  Descriptive  Geometry Large  avo. 


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ELECTRICITY  AND  PHYSICS. 

Anthony  and  Brackett'r  Text-book  of  Physics.    (Magie.) SmaU  8vo, 

Anthony's  Lecture-notes  on  the  Theory  of  Electrical  Measurements ismo, 

Benjamin's  History  of  Electricity 8vo, 

Voltaic  CeU 8vo. 

Classen's  Quantitative  Chemical  Analysis  by  Electirolysis.    (Boltwood.).  .8vo, 

Crehore  and  Squier's  Polarizing  Photo-chronograph »vo, 

Dawson's  "Eneineering"  and  Electric  Traction  Pocket-book. .  lomo,  morocco, 

Flather's  Dvnamometers,  and  the  Measurement  of  Power iimo, 

■Gudc  •  s  D-  Magnete.     (Mottelay.) 8vo, 

H'    r.  a's  Precision  of  Measurements °^°> 

1  lescopic  Mirror-scale  Method,  Adjustments,  and  TesU Large  8vo 

Landauer's  Spectrum  Analysis.    (Tingle.) 8vo, 

Le  Chatelier's  High-temperature  Measurements.  (Boudouard— Burgess.)i2mo, 
LOb's  Electrolysis  and  Electrosynthesis  of  Organic  Compounds.  (Lorenz.)  1  imo, 
«  Lyons's  Treatise  on  Electromagnetic  Phenomena.     Vols.  I.  and  U.  8vo,  each, 

*  Michie.     Elements  of  Wave  Motion  Relating  to  Sound  and  Light 8vo, 

Niaudet's  Elementary  Treatise  on  Electric  Batteries.     (FishoacK.  1 1  Jmo, 

*  ParshaU  and  HobarVs  Electric  Generators SmaU  4to.  half  morocco, 

TRMenberg's'Etectrical  Engineering.   (Haldane  Gee— Kinzbrunner.) . . .   8vo, 
Ryan,  Horris,  and  Hoxie's  Electrical  Machinery.     (.In  preparatiof  ■  • 
Thurston's  SUtionary  Steam-engines ^vo, 

*  TiUman's  Elementary  Lessons  in  Heat 8vo, 

Tory  and  I  itcher's  Manual  of  Laboratory  Physics SmaU  8vo, 


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3  00 


LAW. 

*  Davis's  Elements  of  Law ^^O' 

•  Treatise  on  the  Military  Law  of  United  SUtes 8vo, 

,  Sheep. 

Manual  for  Courts-martial i^mo,  morocco. 

9 


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8vo,    6  oo 
W«lf.  Engineering  and  Architectural  Jurisprudence ^^^^^^    ^  ^^ 

Uw  of  operations  Preliminary  to  Construction  in  E"«-««;°«  «"<>  ^o.    5  oo 

lecture Sheep,    5  50 

8vo,    3  oo 

Lawof  Contracts lamo,    a  50 

Winthrop's  Abridgment  of  MiUtary  Law 


M,i:  I 


iki 


MANUFACTURES. 

Bernadou's  Smokeless  Powder-Nitro-ceUulose  and  Theory  of  the  Cellulose 

Molecule i  jmo, 

Holland's  Iron  Founder lamo, 

"  The  Iron  Founder."  Supplement ■■■  ■■■■■ ' ' '  J^;^  ..  . .  .     .u 

EncyclopedU  of  Founding  and  Dictionary  of  Foundry  Terms  Used  m^e 

Practice  of  Moulding g^^^^ 

Eissler's  Modern  High  Explosives _•  •  g^^'^ 

Effronfs  Enzymes  and  their  AppUcations.     (Presc  .  •-;   V.iSmo. 

Fitzgerald's  Boston  Machinist ^gj^,^ 

Ford's  Boiler  Making  for  Boiler  Makers g^^^ 

Hopkins's  Oil-chemists'  Handbook g^^_ 

SSs^I  5:^;ec;i;;n  and  Analysis  of.Food  with  Special  Reference  to  State 
Control.     (In  preparation.)  ijmo, 

Workshops, 


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Metcalf 's  Steel.     A  Manual  for  Steel-users . 
•s  Cost 
Public  and  Private. 


Metcalfe's  Cost  of  Manufr:tures-And  the   Administration    of    ..—-^^,^. 

4to, 


Meyer's  Modern  Locomotive  Construction ^^^^ 

•  Reisig's  Guide  to  Piece-dyeing g^^^ 

Smith's  Press-working  of  Metals g^^jj  ^^^_ 

Wire:   Its  Use  and  Manufacture ^^^^ 

Thu-SoniManual  of  Steam-boilers,  their  Designs,  Construction  and  Opera- 

tion •  ■  •. gyo, 

Ulke's  Modern  Electrolytic  Copper  Refining ^^^^ 

•  Walke's  1     tures  on  Explosives 

West's  American  Foundry  Practice 

Moulder's  Text-book 

Wiechmann's  Sugar  Analysis 

Wolff's  Windmill  as  a  Prime  Mover 

Woodbury's  Fire  Protection  of  Mills 


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i2mo. 

Small  8vo, 

8vo, 

8vo, 


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MATHEMATICS. 


. .8vo, 
i2mo, 
i2nio, 
i2mo, 


Baker's  Elliptic  Functions 

♦  Bass's  Elements  of  Differential  Calci.'us   

Brigg='s  Elements  of  Plane  Analytic  Geometry . 

Chapman's  Elementary  Course  in  Theory  of  Equations ^^^^^ 

Compton's  Manual  of  Logarithmic  Computations ^^^^ 

Davis's  Introduction  to  the  Logic  of  Algebra —  ^  -^^^^^ 

♦  Dickson's  College  Algebra ,. t  ..„.  .^nir,. 

♦  Introduction  to  the  Theory  of  Algebraic  Equationv    I.«. -e  i-^^^ 

Hateted's  Elements  of  Geometry g^^_ 

Elementary  Synthetic  Geometry 

'10 


50 
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•Johnson's  Three-pUce  LogArithmic  Tables:    Vest-pocket  size P«per, 

10}  copies  for 
«  Mounted  on  heavy  carduoard,  8  X  lo  inches, 

10  copies  for 

Elementary  Treatise  on  the  Intecral  Calculus Small  8vo, 

Curve  Tracing  in  Cartesian  Co-ordinates iimo, 

Treatise  on  Ordinary  and  Partial  Differential  Equations Small  8vo, 

Theory  of  Errors  and  the  Method  of  Least  Squares izmo, 

*  Theoretical  Mechanics i2mo, 

Laplace's  Philosophical  Essay  on  Probabilities.     (Truscott  and  Emory. )  1 2mo, 

•  Ludlow  and  Bass.     Elements  of  Trigonometry  and  Logarithmic  and  Other 

Tables 8vo, 

Trigonometry  and  Tables  published  separately Each, 

Maurer's  Technical  Mechanics.     (In  jireparalion.) 

Merriman  and  Woodward's  Higher  Mathematics 8vo, 

Merriman's  Method  of  Least  Squares 8vo, 

Rice  and  Johnson's  Elementary  Treatise  on  the  Differential  Calculus  Sm.,  8vo, 

Differential  and  Integral  Calculus.     2  vols,  in  one Small  8vo, 

Wood's  Elements  of  Co-ordinate  Geometry 8vo, 

Trigonometry:  Analytical,  Plane,  and  Spherical i2mo. 


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MECHANICAL   ENGINEERING. 

MATERIALS  OF  ENGINEERING,  STEAM-ENGINES  AND  BOILERS. 

Baldwin's  Steam  Heating  for  Buildings 1 2nio, 

Barr's  Kinematics  of  Machinery 8vo, 

*  Bartlett's  Mechanical  Drawing 8vo, 

Benjamin's  Wrinkle?  and  Recipes i2mo. 

Carpenter's  Experimental  Engineering 8vo, 

Heating  and  Ventilating  Buildings 8vo, 

Clerk's  Gas  and  Oil  Engine SmaU  8vo, 

Coolidge's  Manual  of  Drawing 8vo,    paper, 

Cromwell's  Treatise  on  Toothed  Gearing i2mo. 

Treatise  on  Belts  and  Pulleys i2mo, 

Durley's  Kinematics  of  Machines 8vo, 

Flather's  Dynamomettrs  and  the  Measurement  of  Power i2mo, 

Rope  Driving i2mo, 

Gill's  Gas  and  Fuel  Analysis  for  Engineers i2mo. 

Hall's  Car  Lubrication i2mo, 

Hutton's  The  Gas  Engine.     (In  preparation.) 
Jones's  Blachine  Design: 

Part   I. — Kinematics  of  Machinery 8vo, 

Part  II. — Form,  Strength,  and  Proportions  of  Parts 8vo, 

Kent's  Mechanical  Engineer's  Pocket-book i6mo,    morocco, 

Kerr's  Power  and  Power  Transmission 8vo, 

MacCord's  Kinematics;  or.  Practical  Mechanism 8vo, 

Mechanical  Drawing 4to, 

Velocity  Diagrams 8vo, 

Mahan's  Industrial  Drawing.    (Thompson.) 8vo, 

Poole's  Calorific  Power  of  Fuels 8vo, 

Reid's  Course  in  Mechanical  Drawing 8vo, 

Text-Dook  of  Mechanical  Drawing  and  Elementary  Machine  Design     8vo, 

Richards's  Compressed  Air i2mo, 

Robinson's  Principles  of  Mechanism 8vo, 

Smith's  Press^working  of  Metals 8vo, 

Thurston's  Treatise  on    Friction   and    Lost  Work   in    Machinery  and    Mill 
Work 8'n» 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics,  umo, 

11 


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S,  1.   ! 


Wei«b«ch'»  Kinematic*  and  the  Power  of  irarinu" ^^^    ^  ^ 

Klein.) \,."  lli.1. '    fH-rrnuinn— Klein.)    Svo.    5  oo 

Machinery  oJ  Tr.n.mi-ion  and  Governor       Herrmann       ^^^^   ^  ^ 

Hydraulics  and  HydrauUc  Mo*or«.     (Du  Bol..) gvo.    3  oo 

Wolfi'i  WindmiU  at  a  Prime  Mover g^^     a  50 

Wood'i  Turbine* 

MATERIALS  OF  ENGINEERIHG. 

8vo     7  50 
Boveys  Strength  of  Material.  "J ^:°,^;;,J^;rE;:;i„eerin.:    6th  Edition'. 
Burr's  Elasticity  and  ResisUnce  of  the  Material.  01  r,n» ^^^     ^  ^^ 

Rewt • 8vo,    6  00 

Church's  Mechanic,  of  Engineering ^arge  8vo.   6  00 

Johnson'"  MaterUto  of  Construction g,„     ,  50 

Keep's  Cast  Iron 8vo,    7  50 

Lama'.  AppUed  Mechanic..  . . .    ---.  —  '  ;„,„„;„,.). Svo.    7  50 

Marten.'.  Handbook  on  Testing  VMtu*^-  J»*^^"«    8vo,   4  00 

Merriman's  Text-book  on  the  Mechanic,  of  Matenatt       ^^^^^    ^  ^^ 

Strength  of  Material. timo     a  00 

Metcatf ••  SteeL    A  Manual  for  Steel-uwr. ^^^  ^^^^   3  „„ 

Smith'.  Wire:  Ite  Use  and  Manufacture ^^^^     ,  ^o 

Material,  of  Machine. 3  ^oj,  ,  gvo,   8  00 

Thurston's  Material*  of  Engineering g,,,^   3  50 

Part  n.— Iron  and  Steel.  ■_■■■■-  „•  J  • " '  ,  '  ^^  o^er  Alloys  and  their 
Part  UL-A  Treatiw  on  Brawes.  Bronzes,  ano  "xn ^^^^    ^  ^^ 

Con.tituent. . .  .8vo     S  00 

Text-book  of  the  Material,  of  C°°%="°"- "  ^^  ^  Appendix  on  the 

Wood'.  Treatise  on  the  Re.Utance  of  Materml.  and  an  Appe ^^^^    ^  ^ 

Prewrvation  of  Timber gyo^    3  00 

Elements  of  Analytical  Mechanics 

STEAM-EHGINES  AND  BOILERS. 

Carnot's  Reflections  on  the  MoUvePow^^^^^^^^^^^^  \  Z 

Dawson's  "Engineering"  and  Electric   iracno  ^^^^^    ^  ^ 

Ford's  Boiler  Making  for  Boiler  Makers g^^,^    ,  ^ 

Goss's  Locomotive  Sparks ■ •  •  :^  •  U ' " ".  '  i amo,    a  00 

Hemenway's  Indicator  Practice  «><»  S'^-'p^;^^""""^:;   ; Svo.    5  oo 

Button's  Mechanical  Engineering  of  Power  Plants. ...     ^^^^    _.  ^^ 

Heat  and  Heat-engine. gvo.   4  00 

Kent's  Steam-bo'ler  Economy ■■■■ gvo.    150 

Kneass's  Practice  and  Theory  of  the  Injector 8vo.    a  00 

MacCord's  SUde-valves 4to,    10  00 

Meyer's  Modern  Locomotive  Construction . . . .  -  •  -^ ^^^^^    ,  ^^ 

Peabody's  Manual  of  '^'J'"''^-'''^,^^s^^,ni  •otheV  Vapors 8vo.    i  00 

Tables  of  the  Pro.   ^Ztf^Sr^l^ OXi.tr  Be.i-.nt^ne. 8vo.    5  00 

Thermodynamics  of  the  Steam-engine  »i.u  ^^^^    ^  ^^ 

Valve-gears  for  Steam-engines g^^^   ^  00 

Peabody  and  Miller's  Steam-boiler. j^^^  g^^^    ,  50 

Pray's  Twenty  Years  with  »»>;^°^;"*°'„„,„- !„  Gases  and  Saturated  Vapors. 
Pupln's  Thermodynamics  of  Reversible  Cycles  m  oases ^^^^^  ^  ^^ 

(Osterberg.) • ' ' ' ' "  *  Wi-lt '},  i amo.  a  50 

Reagan's  Locomotives:  Slmple.  Compound,  and  Elwtric ^^^^    ^  ^^ 

Ro^gen's  Principles  of  Thermodynam^s-    (^u  Bois  ) . . . .  • „„,.  ,  00 

Sinclair'sLocomotiveEngmeRunningandH^n^^^^^^^^       ^^^^^  ,  3„ 

Smart's  Handbook  of  Engineering  Laboratory  Practice  ^^^^  ^  ^^ 

Snow's  Steam-boiler  Practice •  •  ■ 


Spingler'*  Valve-gear* ""'•    '  S* 

Notes  on  Thermodynamics »»""••    '  "** 

Spangler,  Greene,  and  MarahaU'i  Elementa  o!  Steam-engineering 8vo.    3  oo 

Thurston's  Handy  Table. ;  ■  -»'"•    *  *" 

Manual  of  the  Steam-engine »*<>>»•  8'°'    '°  °° 

Part  I.— History,  Structuce.  and  Theory »»<>•    »  '^ 

Part  n.— Design,  Construction,  and  Operation o'o.   *  <»• 

Handbook  of  Engine  and  Boiler  TrUls,  and  the  Use  of  the  Indicator  and 

the  Prony  Brake S'"'    '  "^ 

Stotlonary  Steam-engines *'*'•    '  ' 

Steam-boiler  Explosions  In  Theory  and  in  Practice lamo,    i  50 

Manual  of  £..eam-bollers,  Their  Designs,  Construction,  and  Operation.  8vo,    5  00 

WeUbach's  Heat,  Steam,  and  Steam-engines.     (Du  Bois.) 8vo.  s  00 

Whitham's  Steam-engine  Design •°'°'  '  °** 

Wilson's  Treatise  on  Steam-boilers.    (FUther.) . . .  i6mo.  a  50 

Wood's  Thermodynamics,  Heat  Motors,  and  Refrigerating  Machines. .    .8vo.  4  00 


MECHANICS  AND  MACHINERY. 

Barr'8  Kinematics  of  Machinery |*°' 

Bovey's  Strength  of  BlaterUls  and  Theory  of  Structures 8vo, 

Chase's  The  Art  of  Pattern-making "°>°' 

Chordal.— Extracts  from  Letters """• 

Church's  Mechanics  of  Engineering 8vo. 

Botes  and  Examples  in  Mechanics ^vo, 

Compton's  First  Lessons  in  MeUl-working umo, 

Compton  and  De  Groodt's  The  Speed  Lathe "mo, 

Cromwell's  Treatise  on  Toothed  Gearing i  jmo, 

Treatise  on  Belts  and  Pulleys iimo. 

Dana's  Text-book  of  Elemenury  Mechanics  for  the  Use  of  Colleges  and 
Schools "'no- 
Dingey's  Machinery  Pattern  Making "m". 

Dredge's  Record  of  the  Transportation   Exhibits  Building  of  the   Worlds 

ColumbUn  Exposition  of  1893 4to,  half  morocco, 

Du  Bois's  Elementary  Principles  of  Mechanics : 

Vol.     I.— Kinematics 8'°> 

Vol.   II.— StoUcs 8'°' 

Vol.  lU.— Kinetics 8vo. 

Mechanics  of  Engineering.     Vol.  I Small  4to. 

Vol.  II Small  4to. 

Durley's  Kmematics  of  Machines 8vo. 

Fitzgerald's  Boston  Machinist '6mo. 

FUther's  Dynamometers,  and  the  Measurement  of  Power lamo, 

Rope  Driving "f""' 

Goss's  Locomotive  Sparks "'°' 

Hall's  Car  Lubrication lamo, 

HoUy's  Art  of  Saw  FiUng '8mo 

♦  Johnson's  Theoretical  Mechanics umo, 

Statics  by  Graphic  and  Algebraic  Methods 8vo. 

Joces's  Blacbine  Design: 

Part  1. — Kinematics  of  Blachlnery 8vo, 

Part  n. — Form,  Strength,  and  Proportions  of  Parts 8vo, 

Kerr's  Power  and  Power  Transmission 8'o» 

Lanza's  Applied  Mechanics *'° 

MacCord's  Kinematics;  or.  Practical  Mechanism 8vo 

Velocity  Diagrams ^'"^• 

Maurer's  Technical  Mechanics,     (/n  preparalion.^ 

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00 

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S       I 


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K--^'-. 


Merrlman".  T.xt-book  on  th.  M.ch.nict  of  lUttrUI.  J^o.    4    ^ 

•  M.ehirt  EtemMtt  of  An.lytic«l  MeehanUi.       .    •  ■  •     •    * 

R..,«i'.LocomotlT..:  Staple.  Compound,  and  Etoctric  -»«o.    a  50 

^•'-isr.::fi;:s«/s^.ndB..«.nu.  a- 

RichMdi'i  Comprewed  Air g^^_    ^  ^^ 

Sobinton't  Principles  of  Mechaniim • ... 

R«n.lforri...ndHoxie'.Electric.lM.cian.ry.     (/n  pr,p«rnrm..> 

Sr'.  Locomotive-engine  Running  .nd  Management  .»-o.    .  00 

Smith'*  Preei-worklng  of  MeUU ^^^^^  ^  ^ 

Materials  of  Blachines •  ■  •  • _,„.., L- 8vo  a  00 

Soangler.  Greene,  and  Marshall's  Elements  of  Steam-engineering.    .  ^   JBvo.  3 

tCton's  Treatise  on  Friction  and  Lost  Work  in  Machinery  -nd  Mijl^^  ^  ^ 

AnimalasaMachine  and  Prime  Motor,  and  the  La,,  of  Energetic.  ,. mo.    .  00 
Warren's  Elements  of  Machine  Construction  and  Drawing  ^  »vo.    7  50 

W:i7bach.f  Kinematics    and    the   Power  of    Transmission.     (Herrmann-    ^  ^ 

Mach^f^el^'^ofTransmissionand  Governors.     (H.rrmann-Klein.).8vo.    500 

Wood's  Element,  of  Analytical  Mechanics ^^^^'    ^   ^^ 

Principles  of  Elementary  Mechanics ^^^^    ^  ^^ 

Turbines '.""."a 4to'.    i  00 

The  World's  Columbian  Exposition  of  1 803 

METALLURGY. 

Egleston's  MetaUurgy  of  Silver.  Gold,  and  Mercury:                                    ^^^  ^  ^^ 

Vol   L-SUver. .  . . '              g^^'  ^  j^ 

Vol   U.-Gold  and  Mercury ,,.:,,                            ,,mo  250 

*»  Iles's  Lead-smelting.     (PosUge  0  cents  additional.) "«».  ^5^ 

Keep's  Cast  Iron _■  - gvo'.  i   50 

v..nh>r<lt's  Practice  of  Ore  Dressing  in  Europe 

S^cttetr'S  temperature Measuremen,s.  (Boudouard-Burg.ss.).»mo.3  o^ 

Metcalf -8  Steel.     A  Manual  for  Steel-users ^^^^'    ^  ^ 

Smith's  MaterUU  of  Machines  ~         n 8vo'  8  00 

Thurston's  MateriaU  of  Engineering.     In  Three  Parts  ^^^.  ^  ^^ 

Part   n.— Iron  and  Steel  ^  i"  '  .'„  a  .u.:^ 

PartlII.-A  TreatUe  on  Brasses.  Bronzes,  and  Other  Alloys  and  th.tr  ^  ^^ 

Constituents 8vo' '^3  00 

Ulke'slModem  Ehctrolytic  Copper  Refining 


MINERALOGY. 

Barringer's  "  escription  of  MineraU  of  Commerci^   Value.     Oblong,  morocco. 

Boyd's  Resources  of  Southwest  Virginia pocket-bookform; 

Map  of  Southwest  Virginia W  ,  j  \  a«n 

Brush's  Manual  of  Determinative  Mineralogy.     (Penfield.)  ^^^     .»vo. 

Chester's  CaUlogue  of  Minerals 'cloth. 

■     Dictionary  of  the  Names  of  Minerals ■ .    \,  ,...u.r' 

Dana's  System  of  Mineralogy L^ge  8vo.  half  leather 

First  Appendix  to  Dana's  New  "System  of  Mineralogy ^"'^    g'°' 

Text-book  of  Mi'-eraiogy 

Minerals  and  How  to  Study  Them ""'O' 

Catalogue  of  American  Localities  of  MineraU Large  »vo. 

Manual  of  Mineralogy  and  Petrography """'• 

Egleston's  Catalogue  of  Minerals  and  Synonyms „    .  ^  ;  c    '  11  all!' 

Hussak's  The  Determination  of  Rock-forming  MineraU.     (Smith.)  Small  8vo. 

14 


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*  Penfield's  Rote*  on  Determinative  Mineralocy  and  Record  of  Mineral  TctU. 

8vo,  paper,  o  50 
Roienbusch't   Microicopical   Phytiocraphy  of   the   Rock-makinc   Minerals. 

( Iddinn.') 8vo,  5  00 

*  Tillman's  Text-book  of  Important  Minerals  and  Docks 8vo,  3  00 

Williams's  Manual  of  Lithology 8vo,  3  00 

MINING. 


Beard's  Ventilation  of  Mines umo, 

Boyd's  Resources  of  Southwest  Virginia 8vo, 

Map  of  Southwest  Virginia Pocket-book  form. 

*  Drinker'i  Tunneling,  Explosive  Compounds,  and  Rock  Drills. 

4to,  half  morocco, 

Elssler's  Modem  High  Explosives 8vo, 

Fowler's  Sewage  Works  Analyses umo, 

Goodyear's  Coal-mines  of  the  Western  Coast  of  the  United  States  i  jmo, 

Ihlseng's  Ma  ual  of  Mining 8vo, 

•*  Iles's  Lead-smelting.     (Postage  oc  additional.)  lamo, 

Kunhardt's  Practice  of  Ore  Dressing  in  Europe 8vo, 

O'Driscoll's  I.'otes  on  the  Treatment  of  Gold  Ores 8vo, 

•  Walke's  Lectures  on  Explosives 8vo, 

Wilson's  Cyanide  Processes i  jmo, 

Chlorination  Process » amo. 

Hydraulic  and  Placer  Mining nmo, 

Treatise  on  Practical  and  Theoretical  Mine  Ventilation i  jmo. 


»  50 

3  00 

2  00 

35  00 

4  00 
2  00 
2  50 
4  00 
2  50 

1  50 

2  00 
4  00 
I  SO 

1  50 

2  00 
I   »5 


SANITARY  SCIENCE. 

Copeland's  Manual  of  Bacteriology.     (In  prep'iritlinv.) 

Folwell's  Sewerage.     (Designing,  Construction,  and  Maintenance.)             8vo,  300 

Water-supply  Engineering. 8vo,  4  00 

Fuertes's  Water  and  Public  Health i imo,  •  50 

Water-filtration   Works i2mo,  2  50 

Gerhard's  Guide  to  Sanitary  House-Inspection i6mo,  i  00 

Goodrich's  Economical  Disposal  of  Town's  Refuse Demy  8vo,  3  50 

Hazen's  Filtration  of  Public  Water-supplies 8vo,  3  00 

Kiersted's  Sewage  Disposal i2mo,  i  25 

Leach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control.     {In  prepanitinrt.) 
Masb.  's   Water-supply.     (Considered    Principally   from    a    Sanitary   Stand- 
point.)    3d  Edition,  Rewritten 8vo,  4  00 

Examination  of  Water.     (Chemical  and  Bacteriological.) i2mo,  i  25 

Merriman's  Elements  of  Sanitary  Engineering 8vo,  2  00 

Nichols's  Water-supply.     (Considered  Mainly  from  a  Chemical  and  Sanitary 

Standpoint.)     (1883.) 8vo,  2  50 

Ogden's  Sewer  Design 1 2mo,  2  00 

*  Price's  Handbook  on  Sanitation i2mo,  i  50 

Richards's  Cost  of  Food.     A  Study  in  Dietaries iimo,  i  00 

Cost  of  Living  as  Modified  by  Sanitary  Science izmo,  i  00 

Richards  and  Woodman's  Air,  Water,  and   Food   from  a  Sanitary  Stand- 
point       8vo,  2  00 

*  Richards  and  Williams's  The  Dietary'Computer 8vo.  i  50 

Rideal's  Sewage  and  Bacterial  Purification  of  Sewage 8vo,  3  50 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  00 

Whipple's  Microscopy  of  Drinking  -.vatef 8vo,  3  50 

WoodhuU's  Notes  and;iMilitary  Hygiene i6.tio,  i  5' 

15 


M.«^       •^.    .. 


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MISCELLANEOUS. 

Barker'!  D«tp-Ma  Soundlnft ;    ■  • ,  ' ' '  ■.''°'  '  **** 

BminoDa't  Owloflcl  Ottld«-book  of  th.  Rocky  MounUln  Eicuiiion  of  th. 

InttrtMtional  CongrtM  of  OtolofUU t«f«  ■▼«>•  '  »• 

TunVt  Popular  Trt«tta«  on  tho  Wlndi '"'•  *  "® 

HAiuM's  American  RaUway  Management  :.••„•;:,■.;•:■,  1'^^°'    ,  „ 

MotfsCompotltion.Dltettibmty.  and  nutritive  Value  of  Foo4.   Mounted  chart,    i  as 

FaUaey  of  the  Pretent  Theory  of  Sound "    •. ' "    „     I, .    '    I  !! 

Rlckettt'aHlttory  of  ReniMlaer  Polytechnic  Inetitute.  i8a4-i8«4.  SmaUSro.    3  oo 

Rotberham-i  UmpnaiUed  Hew  Tetument "^  «^'   »  »» 

Steel's  Treatiae  on  the  DUeaaee  of  the  Dog •»»•   3  ^ 

Tottan't  Important  Question  In  Metrology "™'    '  5° 

The  WorWs  Columbian  Eipositlon  of  1893 *"'    *  "^ 

Worcester  and  AtWnson.  Small  HospiUls.  EsUbUshment  and  Maintenance, 
and  SufgesUons  for  HospiUl  Architecture,  with  Plans  for  a  Smau 
HospiUl """»•    »•» 

HEBREW  AHD  CHALDEE   TEXT-BOOKS. 

Green's  Grammar  of  the  Hebrew  Language •'<>•    ^  »« 

ElemenUry  Hebrew  Grammar »*°^'    '     ' 

Hebrew  Chrestomathy ■  ■  • :  V.      ' 

Gesmlut's  Hebrew  and  Chaldee  Lexicon  to  the  Old  TesUment  Scriptures. 

"*  (TregeUes.) Small  4to.  half  morocco.    500 

LetterU's  Hebrew  Bible "'"•       *' 

16 


^^3^in^Mr£i 


